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The stable module category of a finite group scheme

Banff International Research Station for Mathematical Innovation and Discovery

This talk will be about the representations of a finite group scheme G defined over a field k of positive characteristic. Mimicking the classical local to global principle in commutative algebra, one can tackle some questions concerning these representations by reducing them to questions about p-local p-torsion representations, as p varies over the (not necessarily closed) points in the projective variety defined by the cohomology of G. In recent work we discovered an enhancement of this principle, namely, that the method of passage to generic points in classical algebraic geometry has a counterpart in representation theory that allows one to pass from arbitrary points in the projective variety to closed points. This technique is proving to be quite fruitful. It has lead to a classification of the localising (and also the colocalising) subcategories of the stable module category of G, as well as a form of local Serre duality for the category of finite dimensional representations. The aim of the talk will be to present an overview of these developments. Joint work with Dave Benson, Henning Krause and Julia Pevtsova.

Mathematics; Category theory; homological algebra; Algebraic structures

video/mp4

Author affiliation: University of Utah

2016-12-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60084

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/