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Questa tesi si concentra sulla caratterizzazione di una particolare classe di algebre di Lie che condividono una significativa proprietà coomologica con i gruppi assoluti di Galois di campi. La soluzione affermativa della congettura di Bloch-Kato rivela che i sottogruppi chiusi dei quozienti pro-$p$ massimali dei gruppi assoluti di Galois $G_k(p)$ dei campi $k$ che contengono radici primitive $p$-esime dell'unità hanno coomologia quadratica su $\mathbb F_p$ — ovvero, i loro anelli di coomologia a coefficienti in $\mathbb F_p$ sono generati da elementi di grado $1$, soggetti a relazioni di grado $2$ —, portando alla designazione di tali gruppi come gruppi pro-$p$ di Bloch-Kato. È stato anche congetturato da I. Efrat che, se $G_k(p)$ è finitamente generato, allora ha una struttura specifica, ovvero è di tipo elementare: ciò significa che può essere ottenuto eseguendo iterativamente certi prodotti semidiretti con il gruppo pro-$p$ ciclico infinito $\mathbb Z_p$ e prodotti liberi pro-$p$ partendo dai gruppi Demu\v skin e dal gruppo banale. Le algebre quadratiche rivestono un'importanza significativa nella teoria delle coomologie delle algebre gradate, in quanto formano la parte diagonale dell'anello di coomologia bigraduato. In particolare, nel contesto delle algebre quadratiche, esiste una sottoclasse con un buon comportamento coomologico, note come algebre di Koszul, distinte dal fatto di ammettere risoluzioni lineari libere del modulo banale. A loro volta, ciò è equivalente al fatto che l'anello di coomologia è concentrato sulla sua parte diagonale. I calcoli della coomologia delle algebre di Koszul sono convenientemente realizzati attraverso la cosiddetta costruzione duale di Koszul, che coinvolge semplici calcoli di algebra lineare. Questa caratteristica vantaggiosa rende le algebre di Koszul particolarmente adatte alle analisi coomologiche. Sebbene non tutte le algebre quadratiche siano di Koszul, sorprendentemente, tutte le istanze attualmente conosciut, This thesis focuses on characterizing a specific class of Lie algebras that share a significant cohomological trait with absolute Galois groups of fields. The affirmative solution of the longstanding Bloch-Kato conjecture reveals that closed subgroups of maximal pro-$p$ quotients $G_k(p)$ of absolute Galois groups of fields $k$ containing primitive $p$th roots of $1$ have quadratic $\mathbb F_p$-cohomology — i.e., their $\mathbb F_p$-cohomology rings are generated by elements of degree $1$, subjected to relations of degree $2$—, leading to the designation of such groups as Bloch-Kato pro-$p$ groups. It has also been conjectured by I. Efrat that, if $G_k(p)$ is finitely generated, then it has a specific structure, namely, it is of elementary type, meaning that it can be obtained by iteratively performing certain semidirect products with the infinite cyclic pro-$p$ group $\mathbb Z_p$ and free pro-$p$ products by starting with Demu\v skin groups and the trivial group. Quadratic algebras hold significant importance in the cohomology theory of graded algebras, as they form the diagonal part of the bigraded cohomology ring. Notably, within the realm of quadratic algebras, there exists a well-behaved subset known as Koszul algebras, distinguished by their ability to admit linear free resolutions of the trivial module. In turn, this is equivalent to the fact that the cohomology ring is concentrated on its diagonal part. Computations of the cohomology of Koszul algebras are conveniently achieved through the so-called Koszul dual construction, involving straightforward linear-algebra computations. This advantageous feature makes Koszul algebras particularly amenable to cohomological analyses. Although not all quadratic algebras are Koszul, intriguingly, all currently known instances of Bloch-Kato groups do exhibit Koszul cohomology. This observation prompted T. Weigel and L. Positselski to propose a conjecture asserting that the cohomology of $G_k(p)$, as well as the restric

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p-absolute Galois type, and that the free pro-p product — and, under certain conditions, the direct product — of two pro-p groups of p-absolute Galois type satisfying the Massey vanishing property, is again a pro-p group of p-absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro-p groups of p-absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups.

A. Kurosh's theorem for groups [4] provides the structure of any subgroup of a free product of groups and its proof relies on Bass-Serre theory of groups acting on trees. In the case of Lie algebras, such a general theory does not exist and the analogue of Kurosh theorem is false in general, as it was first noticed by A.I. Shirshov in [10]. However, we prove that, for a class of positively graded Lie algebras satisfying certain local properties in cohomology, such a structure theorem holds true for subalgebras generated by elements of degree 1. Such class consists of Koszul Lie algebras, in which all the subalgebras that are generated in degree 1 are Koszul.

Triplet-bearing ewes and their lambs have the potential to improve flock productivity however, the lack of robust information on optimal nutrition and management is limiting their performance. In comparison to twins, the triplet lamb is; lighter, more metabolically challenged, has lower body temperature, and receives less colostrum and milk which combined results in lower survival rates and weaning weights. While scientifically based management guidelines are available for singletons and twins, guidelines are generally lacking for triplets. Although there is some knowledge on the impacts of nutrition, further studies are required to examine the impacts of varying feeding regimens in pregnancy and lactation, across the body condition range. Characterising the impacts of shelter and other paddock factors, stocking rate, mob size and human intervention would also be of benefit. Future studies must be large enough to allow for evaluation of lamb survival and litter birth weight variation.

To determine the role of Chlamydia trachomatis in miscarriage, we prospectively collected serum, cervicovaginal swab specimens, and placental samples from 386 women with and without miscarriage. Prevalence of immunoglobulin G against C. trachomatis was higher in the miscarriage group than in the control group (15.2% vs. 7.3%; p = 0.018). Association between C. trachomatis-positive serologic results and miscarriage remained significant after adjustment for age, origin, education, and number of sex partners (odds ratio 2.3, 95% confidence interval 1.1-4.9). C. trachomatis DNA was more frequently amplified from products of conception or placenta from women who had a miscarriage (4%) than from controls (0.7%; p = 0.026). Immunohistochemical analysis confirmed C. trachomatis in placenta from 5 of 7 patients with positive PCR results, whereas results of immunohistochemical analysis were negative in placenta samples from all 8 negative controls tested. Associations between miscarriage and serologic/molecular evidence of C. trachomatis infection support its role in miscarriage.

The etiology remains unknown in many cases of bovine abortion in Switzerland. Bacteria of the Chlamydiales order are known abortive agents, therefore cases of bovine abortion from three representative regions of Switzerland were investigated in this study. Particularly Chlamydiaceae as well as the Chlamydia-like organisms Waddlia and Parachlamydia were of interest, especially because of their possible zoonotic potential. Placenta samples (n=343) were tested for these bacteria by different PCR-methods, immunohistochemistry and serology for Chlamydia abortus. Additionally an attempt for the isolation of Waddlia and Parachlamydia was made by co-cultivation in amoebae. In 67.3% of the 343 cases a necrotizing and/or purulent placentitis was found histologically. By real-time PCR, 0.9% (3/343) of the cases were positive for Waddlia, 13.4% (46/343) positive for Parachlamydia and 14.6% (50/343) positive or questionable positive for Chlamydiaceae. Of these samples, confirmation by immunohistochemistry was possible in 2/3 cases for Waddlia, 25/46 for Parachlamydia and 4/50 for Chlamydiaceae. Of the 50 cases positive or questionable positive for Chlamydiaceae, species-identification by ArrayTube Microarray or 16S rRNA PCR resulted in 41 cases positive for C. abortus whereas the presence of Chlamydia suis was confirmed in four and Chlamydia pecorum in one case. This study brought evidence for the importance of different members of Chlamydiales in different regions of Switzerland although Waddlia is not occurring in a high prevalence. On the other hand mixed infections with different Chlamydiales as well as with other abortigenic agents could be found.