Associated primes of Local cohomology modules over Regular rings

Abstract

Let $R$ be an excellent regular ring of dimension $d$ containing a field $K$ of characteristic zero. Let $I$ be an ideal in $R$. We show that $Ass{H}_I^{d-1}(R)$ is a finite set. As an application we show that if $I$ is an ideal of height $g$ with $heightQ=g$ for all minimal primes of $I$ then for all but finitely many primes $P\supseteq I$ with $heightP\ge g+2$, the topological space $Spe{c}^{\circ }(R_P/I{R}_P)$ is connected.

References in corpus (1)

• Local cohomology modules of a smooth Z-algebra have finitely many associated primes