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The parabolic equation describes the propagation of localized waves along the boundary with singularities. Some reformulation of the “separation of variables” scheme is presented, which enables us to obtain a rich set of solutions of the corresponding boundary value problems.

Let X be a smooth connected projective curve over an algebraically closed field, and let S be a finite nonempty closed subset in X. We study deformations of lisse F ‾ l -sheaves on X − S . The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By a dimension counting of this rigid analytic space, we prove a conjecture of Katz which says that a lisse irreducible Q ‾ l -sheaf F on X − S is rigid if and only if dim H 1 ( X , j ⁎ E n d ( F ) ) = 2 g , where j : X − S → X is the open immersion, and g is the genus of X.

We consider the algebraization problem for torsors over a proper formal scheme under a reductive group scheme. Our results apply to the case of semisimple group schemes (which is addressed in detail).

RESUMEN El objetivo del trabajo es caracterizar la responsabilidad social tácita de las organizaciones y destacar la relevancia de las redes informales en su conformación. Dicho tipo de responsabilidad es propio de las organizaciones pequeñas, tradicionales y familiares, y se caracteriza por incorporar en ella aspectos afectivos, culturales y éticos, así como su falta de concreción en un documento formal. Se ilustra la propuesta analítica mediante el estudio cualitativo de dos organizaciones dedicadas a la industria del cacao en el sureste mexicano. Para tal efecto, se realizó un conjunto de entrevistas semiestructuradas, apoyándose además en observación participante y análisis documental. El principal hallazgo consiste en el descubrimiento de una modalidad de responsabilidad social de las organizaciones que no se presenta como una propuesta elaborada racionalmente sino como la expresión tácita de la búsqueda de una identidad social digna, respetuosa tanto del pasado y el futuro como de la cultura y la naturaleza. El trabajo abre una vía de debate sobre la importancia de recuperar valores culturales en la conformación de programas formales de responsabilidad social e incluye además una breve reflexión sobre el potencial de la generalización de los estudios de caso como estrategia metodológica para el estudio de las organizaciones. ABSTRACT This work seeks to characterize tacit social responsibility of organizations and highlight the relevance of informal networks for its emergence. This type of responsibility does not follow a formal scheme, is typical of small, traditional and family organizations, and is characterized by incorporating emotional, cultural, and ethical aspects. Our analytical proposal is exemplified through the qualitative study of two organizations within the cocoa industry in southeastern Mexico. This work also includes a brief reflection on the potential of case studies as methodological strategies for the study of organizations. RESUMO O objetivo do trabalho é caracterizar a responsabilidade social tácita das organizações e destacar a relevância das redes informais em sua formação. Esse tipo de responsabilidade é próprio das organizações pequenas, tradicionais e familiares, e caracteriza-se por incorporar nela aspectos afetivos, culturais e éticos, bem como não apresentar um programa formal. Ilustra-se a proposta analítica mediante o estudo qualitativo de duas organizações dedicadas à indústria do cacau no sudeste mexicano. O trabalho inclui uma breve reflexão sobre o potencial da generalização dos estudos de caso como estratégia metodológica para o estudo das organizações. RÉSUMÉ L'objectif de ce travail est de caractériser la responsabilité sociale implicite des organisations et de souligner la pertinence des réseaux informels dans leur conformation. Ce type de responsabilité est plus typique des petites organisations traditionnelles et familiales, et se caractérise par l'incorporation d'aspects émotionnels, culturels et éthiques, ainsi que par le fait qu'il ne présente pas de programme officiel. La proposition analytique est illustrée par l'étude qualitative de deux organisations du domaine de l'industrie du cacao dans le sud-est du Mexique. Le travail comprend une brève réflexion sur le potentiel de la généralisation des études de cas en tant que stratégie méthodologique pour l'étude des organisations.

We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a $$\delta $$ -structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible groups.

We prove that for any proper smooth formal scheme X over OK, where OK is the ring of integers in a complete discretely valued nonarchimedean extension K of Qp with perfect residue field k and ramification degree e, the i-th Breuil-Kisin cohomology group and its Hodge-Tate specialization admit nice decompositions when ie < p-1. Thanks to the comparison theorems in the recent works of Bhatt, Morrow and Scholze [BMS18], [BMS19], we can then get an integral comparison theorem for formal schemes, which generalizes the case of schemes proven by Fontaine and Messing in [FM87] and Caruso in [Car08]., Nous prouvons que pour tout schéma formel propre et lisse X sur OK, où OK est l’anneau d’entiers dans une extension non-archimédienne complète de valuation discrère K de Qp avec corps résiduel parfait k et degré de ramification e, le i-ème groupe de cohomologie de Breuil-Kisin et sa spécialisation de Hodge-Tate admettent de belles décompositions lorsque ie < p-1. Grâce aux théorèmes de comparaison issus des travaux récents de Bhatt, Morrow and Scholze [BMS18], [BMS19], nous pouvons alors obtenir un théorème de comparaison entier pour des schémas formels, qui généralise le cas des schémas prouvé par Fontaine et Messing dans [FM87] et Caruso dans [Car08].

A clause complex consists of clauses, which are connected by component sharing relations and logic-semantic relations. Hence, clause-complex level structural transformations in translation are concerned with the expression adjustment of these two types of relations. In this paper, a formal scheme for tagging structural transformations in English-Chinese translation is designed. The annotation scheme include 3 steps operated on two grammatical levels: parsing an English clause complex into constructs and assembling construct translations on the clause complex level; translating constructs independently on the clause level. The assembling step involves 2 operations: performing operation functions and inserting Chinese words. The corpus annotation shows that it is feasible to divide structural transformations in English-Chinese translation into 2 levels. The corpus, which unfolds formally the operations of clause-complex level structural transformations, would help to improve the end-to-end translation of complicated sentences.

In this paper we show that it is possible to define a topology on the category of formal schemes over a ring of p-adic integers such that the left adjoint of the Greenberg Transform is a site cocontinuous functor when we equip the category of schemes over the residue field with the etale topology. We show furthermore that this topology allows us to give an isomorphism between the corresponding fundamental groups, and use this isomorphism to show that it is possible to geometrize the quasicharacters of a p-adic torus by a local system on a formal scheme over the ring of p-adic integers.

For a perfect field k k of characteristic p > 0 p>0 and a smooth and proper formal scheme X \mathcal {X} over the ring of integers of a finite and totally ramified extension K K of W ( k ) [ 1 / p ] W(k)[1/p] , we propose a cohomological construction of the Breuil–Kisin module attached to the p p -adic étale cohomology H^i_{\text {\'et}}(X_{\overline {K}},\mathbf {Z}_p). We then prove that our proposal works when p > 2 p>2 , i > p − 1 i > p-1 , and the crystalline cohomology of the special fiber of X \mathcal {X} is torsion-free in degrees i i and i + 1 i+1 .

Since the first optical instruments were invented, the idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope $$ {\mathrm{Env}}_{\varPhi}^{\varOmega}\kern0.5em A $$ in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

Since the first optical instruments were invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope $$ {\mathrm{Env}}_{\Phi}^{\Omega}A $$ in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

We develop a theory of Hodge type Rapoport-Zink formal schemes, which uniformize certain formal completions of the canonical integral models of Shimura varieties of Hodge type at primes of good reduction. We then apply the general theory to the special case of Shimura varieties associated with groups of spinor similitudes, and, in the basic case, determine explicitly the reduced scheme underlying the Rapoport-Zink formal scheme., 66pp, final version, to appear in Compositio Math

The work is devoted to the development of structural approximation algorithms for one-dimensional analysis of raster images of complex surfaces for identifying the spatial coordinates of elements in a surface image. In particular, such surfaces include cellular surfaces of hulls and large shell structures of industrial products. The one-dimensionality of the analysis achieved by synthesizing one-dimensional structural approximation models of all horizontal and vertical lines of the image. The algorithms based on a general formal scheme of structural-approximation synthesis of one-dimensional images of objects with a regular structure, the use of which in various applications considered by the authors earlier in a number of publications. The proposed algorithms allow you to perform spatial identification of cells in the image from the camera. They can be used as part of software for metrological control of industrial products at the stage of preliminary input control. At such a control, gross defects are revealed, leading to disruption of the structure of the cellular surface specified in the design documentation.

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces., 28 pages

In this paper, the constant , which is defined in the letter for a fixed ordinary elliptic curve, is viewed as a special value of formal function on a vast ind-profinite ``Galois cover of the `Hasse Domain' '' parametrizing all ordinary elliptic curves, viewed as a formal scheme.

We define the cotangent complex of a morphism f : X → Y of locally noetherian formal schemes as an object in the derived category D − ( X ) through local homology. We discuss its basic properties and establish the basics results of a deformation theory, providing a characterization of smooth and etale morphisms. This leads to simpler lifting results depending on a differential module, for a class of non-smooth morphism of usual schemes. We also give descriptions of the cotangent complex in the case of regular closed immersions and complete intersection morphisms of formal schemes.

В статье проанализировано значение композиции в портрете с плечевым поясом, включая композиционное решение, формальную схему, эскиз и обобщение. Рассматриваются результаты исследования различных формальных композиционных схем, их влияние на начальный и конечный результат в написании портрета., The article analyzes the meaning of composition in a portrait with a shoulder belt, including a compositional solution, a formal scheme, a sketch and generalization. The author considers the results of various formal composition schemes study, their influence on the initial and final result in painting a portrait., №5 (2018)

We study the Galois descent of semi-affinoid non-archimedean analytic spaces. These are the non-archimedean analytic spaces which admit an affine special formal scheme as model over a complete discrete valuation ring, such as for example open or closed polydiscs or polyannuli. Using Weil restrictions and Galois fixed loci for semi-affinoid spaces and their formal models, we describe a formal model of a $K$-analytic space $X$, provided that $X\otimes_KL$ is semi-affinoid for some finite tamely ramified extension $L$ of $K$. As an application, we study the forms of analytic annuli that are trivialized by a wide class of Galois extensions that includes totally tamely ramified extensions. In order to do so, we first establish a Weierstrass preparation result for analytic functions on annuli, and use it to linearize finite order automorphisms of annuli. Finally, we explain how from these results one can deduce a non-archimedean analytic proof of the existence of resolutions of singularities of surfaces in characteristic zero., Comment: Exposition improved and minor modifications. 37 pages. To appear in Math. Z

Both E–theory and this ring are intimately connected to the infinitesimal deformation theory of formal groups: the associated formal scheme LTh D Spf E h is known as Lubin–Tate space, which classifies deformations of € [15]. More precisely, when R is a complete local ring with residue field k , maps Spf R ! LTh are in bijective correspondence with ?–isomorphism classes of formal group laws over R which reduce over the special fiber to the specified formal group law € . Given a complex orientation Spf E h CP S Spf E h ŒŒx of E–theory, the resulting formal group law associated to the formal group

Although mentoring has become increasingly popular within UK higher education, there is little evaluative research. The current longitudinal study aimed to evaluate the usage of a peer mentoring scheme during a first semester at university amongst 124 students. Results indicate that during the first week at university the majority accessed the scheme but this then diminished by 10 weeks. There were strong positive correlations among contact, satisfaction and perceived mentor social support. Additionally, expectations of mentoring mediated the relationship between contact time and satisfaction. Correlations with student well-being and intention to withdraw, however, indicated that students reporting high levels of mentor support were worse off than those reporting less support. Students wanting more support from mentors were significantly lower on levels of integration and well-being. Findings suggest a potentially vulnerable group of students who access and use the mentoring scheme because of the problems...

We study tropical geometry in the global setting using Berkovich's deformation retraction. We state and prove the generalized balancing conditions in this setting. Starting with a strictly semi-stable formal scheme, we calculate certain sheaves of vanishing cycles using analytic \'etale cohomology, then we interpret the tropical weights via these cycles. We obtain the balancing condition for tropical curves on the skeleton associated to the formal scheme in terms of the intersection theory on the special fiber. Our approach works over any complete discrete valuation field., Comment: 19 pages. I added an example for a K3 surface, revised the definition of tropical weights, and completed the bibliography

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

Let ${\mathfrak o}$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ and ${\mathfrak X}_0$ a smooth formal scheme over the formal spectrum of ${\mathfrak o}$. Given an admissible formal blow-up ${\mathfrak X}$ of ${\mathfrak X}_0$ we introduce sheaves of differential operators ${\mathscr D}^\dagger_{{\mathfrak X},k}$ on ${\mathfrak X}$, for every integer $k \ge k_{\mathfrak X}$, where $k_{\mathfrak X}$ depends on the blow-up morphism ${\mathfrak X}\rightarrow {\mathfrak X}_0$. This generalizes Berthelot's construction of sheaves of arit hmetic differential operators on ${\mathfrak X}_0$. The coherence of these sheaves and several other basic properties are proven. In the second part we study the projective limit sheaf ${\mathscr D}_{{\mathfrak X},\infty} = \varprojlim_k {\mathscr D}^\dagger_{{\mathfrak X},k}$ and so-called coadmissible modules for ${\mathscr D}_{{\mathfrak X},\infty}$. The inductive limit of the sheaves ${\mathscr D}_{{\mathfrak X},\infty}$, over all admissible blow-ups ${\mathfrak X}$ of ${\mathfrak X}_0$, gives rise to a sheaf ${\mathscr D}_{\langle {\mathfrak X}_0 \rangle}$ on the Zariski-Riemann space of ${\mathfrak X}_0$. Analogues of Theorems A and B are shown to hold in each of these settings, i.e., for ${\mathscr D}^\dagger_{{\mathfrak X},k}$, ${\mathscr D}_{{\mathfrak X},\infty}$, and ${\mathscr D}_{\langle {\mathfrak X}_0\rangle}$., Comment: Some error corrected and some examples added

The Wright–Fisher model considers the effects of sampling for the distribution of alleles across discrete generations. Although the model is usually formulated for diploid populations, and some of the interesting effects occurring in generalizations depend on that diploidy, the formal scheme emerges already for haploid populations. In the basic version, with which we start here, there is a single genetic locus that can be occupied by different alleles, that is, alternative variants of a gene. In the haploid case, it is occupied by a single allele, whereas in the diploid case, there are two alleles at the locus. Biologically, diploidy expresses the fact that one allele is inherited from the mother and the other from the father. However, the distinction between female and male individuals is irrelevant for the basic model.

Biological individuals are usually defined by evolutionists through a reference to natural selection. This article looks for a concept of individuality that would hold at the same time for organisms and for communities or ecosystems, the latter being unaffected by natural selection (as it is usually contended). In the wake of Simon’s notion of “quasi-independence,” I elaborate a concept of “weak individuality” defined by probabilistic connections between sub-entities, read off our knowledge of their interactions. This formal scheme of connections allows one to infer what are the individuals in the domain addressed by the theory of the interactions. The article argues that if ecosystems do not have strong individuality (in the sense of natural-selection-based individuality), they still possess a weak individuality, ecological theories providing the values of the variables in the formula for individuality.

The purpose of the article is to show how useful Sraffa’s formal scheme is for a critical study of classical economists in general and Quesnay’s Tableau économique in particular. Sraffa’s parsimonious argumentation offers a strong incentive to generalise his framework and suggest the idea of a classical system of prices whose prices of production would be a special case. To elaborate a clear notion of a classical system of prices relevant for the study of a priori different authors is the first objective of this article. In this view, the basic elements of a classical system of prices are distinguished: technique of production, rule of imputation of the price of surplus and conditions of reproduction. Even if this may help to have a fresh look on some authors like Petty or Cantillon, it is certainly (with the obvious exception of Ricardo and Torrens) about Quesnay and his Tableau économique that the idea of a classical system of prices is the most fruitful. To suggest a renewed reading of the Tableau is the second objective of the present article.

This analysis introduces a generalization of the basic statistical concepts of expectation values and variance for non-Euclidean metrics induced by Lp-norms. The non-Euclidean Lp means are defined by exploiting the fundamental property of minimizing the Lp deviations that compose the Lp variance. These Lp expectation values embody a generic formal scheme of means characterization. Having the p-norm as a free parameter, both the Lp-normed expectation values and their variance are flexible to analyze new phenomena that cannot be described under the notions of classical statistics based on Euclidean norms. The new statistical approach provides insights into regression theory and Statistical Physics. Several illuminating examples are examined.

Orbital-based exchange (x) correlation (c) energy functionals, leading to the Optimized Effective Potential (OEP) formalism of density-functional theory (DFT), are gaining increasing importance in ground-stateDFT, as applied to the calculation of the electronic structure of closed systems with a fixed number of particles, like atoms and molecules. These types of functionals prove also to be extremely valuable for dealing with solid-state systems with reduced dimensionality, such as is the case ofelectrons trapped at the interface between two different semiconductors, or narrow metallic slabs.In both cases, electrons build a quasi-two-dimensional electron gas, or Q2DEG.We provide here a general DFT-OEP formal scheme valid both for Q2DEG´s either isolated (closed) or in contact with a particle bath (open), and show that both possible representations are equivalent, being the choice of one or the other essentially a question of convenience. Based on this equivalence, a calculation scheme is proposed which avoids the non-invertibility problem of the density response function forclosed systems.We also consider the case of spontaneously spin-polarized Q2DEG´s, and findthat far from the region where the Q2DEG is localized, the exact $x$-only exchange potential approaches two different, spin-dependent asymptotic limits. As an example, besides these formal results, we also provide numerical results for a spin-polarized jellium slab, using the new OEP formalism for closed systems. The accuracy of the Krieger-Li-Iafrate (KLI) approximation has been also tested for the same system, and found to be as good as it is for atoms and molecules. Fil: Rigamonti, Santiago. Humboldt-Universität zu Berlin; Alemania Fil: Horowitz, Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina Fil: Proetto, Cesar Ramon. Comisión Nacional de Energía Atomica. Centro Atomico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

We complete the study of the supersingular locus $\mathcal{M}^{\mathrm{ss}}$ in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n−1) over ℚ in the case that p is inert. This was started by the first author in Can. J. Math. 62, 668–720 (2010) where complete results were obtained for n=2,3. The supersingular locus $\mathcal{M}^{\mathrm{ss}}$ is uniformized by a formal scheme $\mathcal{N}$ which is a moduli space of so-called unitary p-divisible groups. It depends on the choice of a unitary isocrystal N. We define a stratification of $\mathcal{N}$ indexed by vertices of the Bruhat-Tits building attached to the reductive group of automorphisms of N. We show that the combinatorial behavior of this stratification is given by the simplicial structure of the building. The closures of the strata (and in particular the irreducible components of $\mathcal{N}_{\mathrm{red}}$ ) are identified with (generalized) Deligne-Lusztig varieties. We show that the Bruhat-Tits stratification is a refinement of the Ekedahl-Oort stratification and also relate the Ekedahl-Oort strata to Deligne-Lusztig varieties. We deduce that $\mathcal{M}^{\mathrm{ss}}$ is locally a complete intersection, that its irreducible components and each Ekedahl-Oort stratum in every irreducible component is isomorphic to a Deligne-Lusztig variety, and give formulas for the number of irreducible components of every Ekedahl-Oort stratum of $\mathcal{M}^{\mathrm{ss}}$ .

The purpose of this study was to investigate students' scheme in solving mathematics problems. Scheme are data structures for representing the concepts stored in memory. In this study, we used it in solving mathematics problems, especially ratio and proportion topics. Scheme is related to problem solving that assumes that a system is developed in the human mind by acquiring a structure in which problem solving procedures are integrated with some concepts. The data were collected by interview and students' written works. The results of this study revealed are students' scheme in solving the problem of ratio and proportion as follows: (1) the content scheme, where students can describe the selected components of the problem according to their prior knowledge, (2) the formal scheme, where students can explain in construct a mental model based on components that have been selected from the problem and can use existing schemes to build planning steps, create something that will be used to solve problems and (3) the language scheme, where students can identify terms, or symbols of the components of the problem.Therefore, by using the different strategies to solve the problems, the students' scheme in solving the ratio and proportion problems will also differ.

For several decades, the plastic deformation mechanisms of f.c.c. metals under cyclic loading have received considerable attention. The extensive work on this subject has gradually lead to the identification of the physical processes to be included in a formal scheme of fatigue behavior. Accordingly, we propose a review of the physical mechanisms of plastic deformation in f.c.c. metals and alloys to define the state-of-the-art and motivate future studies. The aim is to demonstrate the importance of a good knowledge of the heterogeneous nature of deformation at the intra-granular scale in defining a physical model of cyclic behavior. A large characterization of the different stages associated with the evolution of heterogeneous dislocation structures during tensile and cyclic loadings is given for an austenitic stainless steel AISI 316L. A unified view of these various structures is proposed in the form of a modified Pedersen's map [e max = f(e pcum ), where e max is the maximum plastic strain and e pcum the cumulative plastic strain] in the case of tensile loading and different kinds of cyclic loading: uni-axial and multi-axial tests under stress or strain amplitude control. The specificities of each domain defined in the map are discussed in terms of long-range internal stresses in order to formalize, in a simple composite scheme, the intra-granular stress-strain field. The importance of taking into account this scheme and the nature of the different dislocations populations in a polycrystalline model is illustrated.

We consider the algebraization problem for principal bundles with reductive structure group, defined on the complement of a closed subset Z in a proper formal scheme. We show that, when Z is of codimension at least 3, an algebraization always exists. For codimension 2 we show that an algebraization exists precisely when a certain additional condition is satisfied.

Here we consider a model of quantum computation, based on the monodromy representation of a Fuchsian system. The role of local and entangling operators in monodromic quantum computing is played by monodromy matrices of connections with logarithmic singularities acting on the fiber of a holomorphic vector bundle as on the space of qubits. The leading theme is the problem of constructing a set of universal gates as monodromy operators induced from a connection with logarithmic singularity. In the formal scheme developed by us, already known models — topological and holonomic — can be incorporated.

This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale cohomology of these spaces realizes simultaneously the local Langlands and Jacquet-Langlands correspondences. The proofs given so far use Drinfeld modular varieties or Shimura varieties to derive this local result. In this paper we show without the use of global moduli spaces that the Jacquet-Langlands correspondence for supercuspidal representations is realized by the Euler-Poincare characteristic of the cohomology. Under a certain finiteness assumption on the cohomology groups, it is shown that the correspondence is realized in only one degree. One main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the deformation spaces., Comment: 72 pages, 1 figure, submitted

Let V be a complete discrete valuation ring with residue field k of characteristic p > 0 and fraction field K of characteristic zero. Let S be a formal scheme over V and let X -> S be a locally projective formal abelian scheme. In this paper we prove that, under suitable natural conditions on the Hasse-Witt matrix of X circle times(V) V/pV, the kernel of the Frobenius morphism on X-k can be canonically lifted to a finite and flat subgroup scheme of X over an admissible blow-up of S, called the 'canonical subgroup of X'. This is done by a careful study of torsors under group schemes of order p over X. We also present a filtration on H-1 (3C, mu(p)) in the spirit of the Hodge-Tate decomposition.

We describe the mod $p^r$ pro $K$-groups $\{K_n(A/I^s)/p^r\}_s$ of a regular local $\mathbb F_p$-algebra $A$ modulo powers of a suitable ideal $I$, in terms of logarithmic Hodge-Witt groups, by proving pro analogues of the theorems of Geisser-Levine and Bloch-Kato-Gabber. This is achieved by combining the pro Hochschild-Kostant-Rosenberg theorem in topological cyclic homology with the development of the theory of de Rham-Witt complexes and logarithmic Hodge-Witt sheaves on formal schemes in characteristic $p$. Applications include the following: the infinitesimal part of the weak Lefschetz conjecture for Chow groups; a $p$-adic version of Kato-Saito's conjecture that their Zariski and Nisnevich higher dimensional class groups are isomorphic; continuity results in $K$-theory; and criteria, in terms of integral or torsion etale-motivic cycle classes, for algebraic cycles on formal schemes to admit infinitesimal deformations. Moreover, in the case $n=1$, we compare the etale cohomology of $W_r\Omega^1_\text{log}$ and the fppf cohomology of $\mathbf\mu_{p^r}$ on a formal scheme, and thus present equivalent conditions for line bundles to deform in terms of their classes in either of these cohomologies.