We investigate infinite-dimensional modules for a linear algebraic group πΎ over a field of positive characteristic p. For any subcoalgebra C β πͺ(πΎ) of the coordinate algebra of πΎ, we consider the abelian subcategory CoMod(C) β Mod(πΎ) and the left exact functor (β)C : Mod(πΎ) β CoMod(C) that is right adjoint to the inclusion functor. The class of cofinite πΎ-modules is introduced using finite-dimensional subcoalgebras of πͺ(πΎ). We categorify a construction of Hardesty-Nakano-Sobaje, thereby supplementing cofinite type in providing invariants for proper mock injective πΎ-modules.
This video is part of the conference Representation Theory and Geometry that took place at the University of Georgia.
