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

### Abstract

Let \$(R,m)\$ be a local Noetherian ring, let \$I\subset R\$ be any ideal and let \$M\$ be a finitely generated \$R\$-module. In 1990 Craig Huneke conjectured that the local cohomology modules \$H^i_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\$.\u

Publisher: Elsevier
Year: 2002
OAI identifier: oai:eprints.whiterose.ac.uk:10159

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