Sep 15 2021

# Commutative Algebra Seminar: Annihilating local cohomology modules and the weak implies strong conjecture, by Thomas Polstra

September 15, 2021

3:00 PM - 3:50 PM

Zoom

Chicago, IL

## Calendar

Thomas Polstra (University of Virginia): Annihilating local cohomology modules and the weak implies strong conjecture

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.

Wenliang Zhang

Sep 28, 2021

Sep 28, 2021