On the local cohomology of modular invariants

TL;DR

This paper investigates the local cohomology of modular invariant rings, providing computations of numerical invariants and exploring properties like Cohen-Macaulayness, with applications highlighting differences between local and global cases.

Contribution

It offers new computations of local cohomology invariants for modular invariants and analyzes their Cohen-Macaulay properties, emphasizing the local case distinctions.

Findings

Computed numerical invariants of local cohomology for modular invariants

Analyzed Cohen-Macaulay and related properties in the local setting

Highlighted differences between local and global invariant cases

Abstract

We compute some numerical invariants of local cohomology of the ring of invariants by a finite group, mainly in the modular case. Also, we present some applications. In particular, we study Cohen-Macaulay property of modular invariants from the viewpoints of depth, Serre's condition and the relevant generalizations (e.g., the Buchsbaum property, etc). The situation in the local case is different from the global case.