Jordan Types for Indecomposable Modules of Finite Group Schemes

TL;DR

This paper explores the relationship between geometric invariants called π-points and the structure of the stable Auslander-Reiten quiver in finite group schemes, revealing new invariants and insights into module categories.

Contribution

It introduces new invariants of the AR-quiver derived from π-points and analyzes their relation to specific module types within the quiver.

Findings

π-points induce new invariants of the AR-quiver

combinatorial properties of AR-components relate to π-points

analysis of components with Carlson, supported, and endo-trivial modules

Abstract

In this article we study the interplay between algebro-geometric notions related to $\pi$-points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that $\pi$-points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on $\pi$-points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial modules.