Associated primes of local cohomology after adjoining indeterminates. II: The general case (Q502916)

Let \(A\) be a field of characteristic \(0\), \(R\) a formal power series ring over \(A\) and \(I \subset R\) an ideal. Then \textit{G. Lyubeznik} showed that the local cohomology module \(H^j_I(R)\) has only finitely many associated primes [Invent. Math. 113, No. 1, 41--55 (1993; Zbl 0795.13004)]. In the present paper, the author tried to weaken the assumption of \(A\) by using the resolution of singularities of \(\mathrm{Spec } A\). One of his result is the following. Let \(A\) be a finitely generated algebra over a field of characteristic \(0\), \(R\) a formal power series ring or a polynomial ring over \(A\), and \(I \subset R\) an ideal. Assume that \(A\) is a normal domain and that \(A\) has an isolated singularity. Then the local cohomology module \(H_I^j(R)\) has finitely many associated primes.