Commutative Algebra Seminar
Thomas Polstra
University of Virginia
Annihilating local cohomology modules and the weak implies strong conjecture
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.
Wednesday September 15, 2021 at 3:00 PM in Zoom