A remarkable functor on $G$-modules

TL;DR

The paper introduces a novel tensor functor on categories of modular representations of reductive algebraic groups with unique properties, linking it to recent conjectures and hypercohomology.

Contribution

It presents a new functor with remarkable properties, including tensoriality and mapping standard objects to one-dimensional objects, and connects it to ongoing research and conjectures.

Findings

Functor is tensorial and maps standard objects to one-dimensional objects

Connects the functor to recent work of Gruber and hypercohomology

Proposes a conjecture relating the functor to the Finkelberg-Mirkovic equivalence

Abstract

We introduce a new functor on categories of modular representations of reductive algebraic groups. Our functor has remarkable properties. For example it is a tensor functor and sends every standard and costandard object in the principal block to a one-dimensional object. We connect our functor to recent work of Gruber and conjecture that our functor is equivalent to hypercohomology under the equivalence of the Finkelberg-Mirkovic conjecture.