Local duality for representations of finite group schemes

TL;DR

This paper establishes a duality theorem for the stable module category of finite group scheme representations, leading to Serre duality analogues and Auslander-Reiten triangles in localized subcategories.

Contribution

It introduces a duality theorem for the stable module category of finite group schemes, extending classical dualities and structural results in representation theory.

Findings

Proves a duality theorem for the stable module category.

Derives an analogue of Serre duality.

Establishes Auslander-Reiten triangles in localized subcategories.

Abstract

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the stable category, for each homogeneous prime ideal $\mathfrak{p}$ in the cohomology ring of the group scheme.