Demazure descent and representations of reductive groups

TL;DR

This paper introduces Demazure descent data on triangulated categories and demonstrates its application by showing how it relates the derived categories of representations of a reductive algebraic group G and its Borel subgroup B.

Contribution

It formalizes Demazure descent data and establishes an equivalence between the descent category and the derived category of G-representations.

Findings

Demazure functors form descent data on derived categories of B-representations.

The descent category is equivalent to the derived category of G-representations.

Provides a new categorical framework for understanding reductive group representations.

Abstract

We introduce the notion of Demazure descent data on a triangulated category C and define the descent category for such data. We illustrate the definition by our basic example. Let G be a reductive algebraic group with a Borel subgroup B. Demazure functors form Demazure descent data on the derived category of Rep(B) and the descent category is equivalent to the derived category of Rep(G).