An example of an infinite set of associated primes of a local cohomology module

2002/09/25 by Mordechai Katzman · 2 citations
Mathematics · #math.AC #math.AG #msc:13D45 #msc:13E05 #msc:13A02 #msc:13P99

paper · pdf

published as Journal of Algebra, 252 (2002) pp. 161-166

arxiv created 2002/09/25 · arxiv updated 2009/11/30

Abstract

Let (R,m) be a local Noetherian ring, let I⊂ R be any ideal and let M be a finitely generated R-module. In 1990 Craig Huneke conjectured that the local cohomology modules Hⁱ_I(M) have finitely many associated primes for all i. In this paper I settle this conjecture by constructing a local cohomology module of a local k-algebra with an infinite set of associated primes, and I do this for any field k.

Cited by

• Koszul cohomology and support of local cohomology modules of complete intersections
• Local cohomology modules with nonclosed support

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