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

2012/03/20 by Marc Chardin, Chardin, Marc, Jean-Pierre Jouanolou +3 · 2 citations
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1203.4342

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

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• Betti splittings for powers of sums of ideals
• On the structure of sequentially Cohen--Macaulay bigraded modules

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• On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules
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