On the local cohomology of modular invariants

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.