Associated primes of local cohomology modules and of Frobenius powers

By Anurag Singh, Irena Swanson. 2004

92 citations recorded by the source corpus.

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities as well as F-regular unique factorization domains of positive characteristic. As a consequence, we answer a question on the associated primes of Frobenius powers of ideals, which arose from the localization problem in tight closure theory.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/edd0b142aab3ed5cb4ddd3c6852ec48c68f8fd97

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In Algebra and Number Theory

1. K. Divaani-Aazar
2. A. Mafi
3. M. Dibaei
4. Siamak Yassemi

In Geometry and Topology

1. K. Divaani-Aazar
2. A. Mafi
3. M. Dibaei
4. Siamak Yassemi

Citations in the corpus

• Associated Primes of Local Cohomology Modules of Weakly Laskerian Modules (2005, background): “For each i ≥ 0, the ith local cohomology module of M with respect to is defined as Hi M = lim−→ n ExtiR R/ n M The reader can refer to Brodmann and Sharp (1998) for basic properties of local cohomology.”