Gluing Borel-Smith functions and the group of endo-trivial modules

TL;DR

This paper characterizes the group of endo-trivial modules for a p-group by relating it to the obstruction group associated with gluing Borel-Smith functions, providing a new perspective in modular representation theory.

Contribution

It introduces a novel approach connecting endo-trivial modules with the gluing problem of Borel-Smith functions, offering a deeper understanding of their structure.

Findings

Describes the group of endo-trivial modules in terms of an obstruction group.

Establishes a link between endo-trivial modules and Borel-Smith functions.

Provides a framework for analyzing endo-trivial modules via gluing problems.

Abstract

The aim of this paper is to describe the group of endo-trivial modules for a $p$-group $P$, in terms of the obstruction group for the gluing problem of Borel-Smith functions.