Abstract
Let $A$ be a domain finitely generated as an algebra over a field, $k$ of characteristic zero, $ R=A[t_1,\dots ,t_\ell ]\quad \mbox {or}\quad A[[t_1,\dots ,t_\ell ]]$, and $I$ an ideal of $R$. If $A$ has a resolution of singularities, $Y_0$, which is the blowup of $A$ along an ideal of depth at least 2 and is covered by a finite number of open affines with $H^j(Y_0,\mathcal {O}_{Y_0})$ of finite length over $A$ for $j>0$, we prove that $\rm{Ass} _RH^i_I(R) $ is finite for every $i$. In particular, this holds when $A$ is a finite-dimensional normal domain with an isolated singularity which is a finitely generated algebra over a field of characteristic~0.
Citation
Hannah Robbins. "Associated primes of local cohomology after adjoining indeterminates. Part 2: The general case." J. Commut. Algebra 8 (4) 589 - 598, 2016. https://doi.org/10.1216/JCA-2016-8-4-589
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