Module Invariants and Blocks of Finite Group Schemes

TL;DR

This paper explores the topological and geometric structures associated with blocks of finite group schemes, focusing on cohomological support varieties and their representation-theoretic aspects.

Contribution

It introduces new insights into the topological spaces linked to blocks of finite group schemes, combining cohomological and representation-theoretic methods.

Findings

Identification of new topological invariants for blocks

Connections between support varieties and representation theory

Enhanced understanding of the geometric structure of blocks

Abstract

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the representation-theoretic constructions of E. Friedlander and J. Pevtsova.