THE EVENTUAL STABILITY OF DEPTH, ASSOCIATED PRIMES AND COHOMOLOGY OF A GRADED MODULE

Abstract

The asymptotic stability of several homological invariants of the graded\npieces of a graded module has attracted quite a lot of attention over the last\ndecades. We provide in this text several stability results together with\nestimates of the degree from which it stabilizes. Before we establish these\nregularity results, we prove several facts about depth and cohomological\ndimension with respect to a finitely generated ideal and about\nCastelnuovo-Mumford regularity of a graded module.\n