Rational Cohomology and Supports for Linear Algebraic Groups

TL;DR

This paper introduces an extension of support variety theory from finite group schemes to representations of linear algebraic groups, aiming to deepen understanding and facilitate future research in the area.

Contribution

It extends the support variety framework to linear algebraic groups, providing foundational insights and clarifications for this broader class of representations.

Findings

Extended support variety theory to linear algebraic groups

Clarified key concepts and simplified existing literature

Outlined future research directions in the field

Abstract

This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the "theory of support varieties" which has proved successful in the study of representations of finite group schemes. The lectures offer readers an introduction to the subject together with "homework problems, simplify and clarify some points in the literature, and mention some directions for future research.