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We develop a support theory for elementary supergroup schemes, over a field of positive characteristic p ≥ 3, starting with a definition of a π-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and π-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra k[t,τ]/(tp−τ2), where t has even degree and τ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme. [ABSTRACT FROM AUTHOR]

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the p-local and p-torsion subcategories of the stable category, for each homogeneous prime ideal p in the cohomology ring of the group scheme. [ABSTRACT FROM AUTHOR]

This is a report on recent work of Chałupnik and Touzé. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors. [ABSTRACT FROM PUBLISHER]

Tilting and cotilting modules are classified for the completed path algebra of a quiver of type A˜n with linear orientation. This classification problem arises naturally in the classification of cotilting modules over certain associative algebras (Pacific J. Math. 211 (2003) 41–60). The combinatorics of the collection of all tilting and cotilting modules is described in terms of Stasheff associahedra. [Copyright &y& Elsevier]

The notion of tameness for the derived category of a finite dimensional algebra is introduced and standard properties are established. This is based on classical tameness definitions of Drozd and Crawley-Boevey for the category of finite dimensional representations. [ABSTRACT FROM AUTHOR]

Abstract: The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring . [Copyright &y& Elsevier]