Commutative Algebra Seminar

Spring 2020, Friday 2:30–3:20, LCB 215

Date Speaker Title — click for abstract
February 14 Akhil Mathew
University of Chicago
The arc-topology
I will discuss a Grothendieck topology on the category of quasi-compact quasi-separated schemes called the "arc-topology." Covers in the arc-topology are tested via rank <=1 valuation rings. This topology is motivated by classical questions in algebraic K-theory, and leads to Mayer-Vietoris style sequences. Our main result is that étale cohomology with torsion coefficients satisfies arc-descent. This is joint work with Bhargav Bhatt.
February 21 Thomas Polstra
University of Utah
A theorem about maximal Cohen-Macaulay modules
In this talk we will discuss a surprising uniform property concerning the class of Cohen-Macaulay modules over strongly F-regular rings. As an application, we show that the torsion subgroup of the divisor class group of a local strongly F-regular ring is finite.
February 28 Gregory Taylor
University of Illinois at Chicago
Inversion of adjunction for F-signature
Strongly F-regular inversion of adjunction is the positive characteristic analog of the klt/plt inversion of adjunction in birational geometry. In characteristic 0, the klt/plt inversion of adjunction statement can made quantitative with the normalized volume. In this talk, we discuss an analogous quantitative refinement of strongly F-regular inversion of adjunction via the F-signature. 
March 4, **Wednesday** LCB 323 Florian Enescu
Georgia State University
March 13 Spring Break
March 20 Henning Krause
University of Bielefeld
March 27
April 3 Hiroki Matsui
April 10 James Cameron
April 17 Ben Elias
University of Oregon

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