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

By Mordechai Katzman. 2002

117 citations recorded by the source corpus.

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 $k$.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a2642ef8bdc6e72658108071af615d94914f4c33

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In Algebra and Number Theory

1. M. Dibaei
2. Siamak Yassemi
3. Le Thanh Nhan
4. Cameron Wickham

In Geometry and Topology

1. M. Dibaei
2. Siamak Yassemi
3. Le Thanh Nhan
4. Cameron Wickham

Citations in the corpus

• Cofiniteness of local cohomology modules for ideals of small dimension (2009, unknown): “[18]).”
• Associated primes and cofiniteness of local cohomology modules (2004, background): “But K is a quotient of H i (R/p + bR), which is m-cofinite by hypothesis, so K is also m-cofinite.”
• ON GENERALIZED REGULAR SEQUENCES AND THE FINITENESS FOR ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES (2005, background): “Recently, Singh (2000) (in the nonlocal case) and Katzman (2002) (in the local case) have given examples to show that AssHiI M is generally not a finite set.”