Examples of local Cohomology Modules for Ramified Regular Local Rings having Finite Set of Associated Primes

2015/12/17 by Bhattacharyya, Rajsekhar
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.05695

Abstract

Lyubeznik's conjecture, (\citeLy1, Remark 3.7) asserts the finiteness of the set ssociated primes of local cohomology modules for regular rings. But, in the case of ramified regular local ring, it is open. Recently, in Theorem 1.2 of \citeNu1, it is proved that in any Noetherian regular local ring S and for a fixed ideal J⊂ S, associated primes of local cohomology Hⁱ_J(S) for i≥ 0 is finite, if it does not contain p. In this paper, we use this result to construct examples of local cohomology modules for ramified regular local ring so that they have finitely many associated primes.

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