Thomas Polstra : Annihilating local cohomology modules and the weak implies strong conjecture

Posted by Wenliang Zhang , part of the Commutative Algebra Seminar.

At

Sept. 15, 2021, 3 p.m.

In

Zoom

Abstract

Let $(R,\mathfrak{m},k)$ be local normal Cohen-Macaulay domain and $I\subseteq R$ an ideal of pure height $1$. For each natural number $N$ let $I^{(N)}$ denote the $N$th symbolic power of $I$. We consider annihilators of the local cohomology modules $H^i_{\mathfrak{m}}(R/I^{(N)})$. When $R$ is of prime characteristic $p>0$ and $I$ is a multiple of an anticanonical ideal of $R$ then understanding the annihilators $H^{i}_{\mathfrak{m}}(R/I^{(p^e)})$ as $e$ varies through the natural numbers sheds light on the weak implies strong conjecture from tight closure theory. This talk is based on joint work with Ian Aberbach.