A note on the associated primes of local cohomology modules for regular local rings

Authors : Yubin GAO

Pages : 2775-2778

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_Iinsert ignore into journalissuearticles values(R);$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{insert ignore into journalissuearticles values(x,y,z);}insert ignore into journalissuearticles values(R);$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik`s conjecture is true in the regular local rings case.
Keywords : Local cohomology modules, associated primes, regular local rings