  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.
