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