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 arctopology
I will discuss a Grothendieck topology on the category of quasicompact quasiseparated schemes called the "arctopology." Covers in the arctopology are tested via rank <=1 valuation rings. This topology is motivated by classical questions in algebraic Ktheory, and leads to MayerVietoris style sequences. Our main result is that étale cohomology with torsion coefficients satisfies
arcdescent. This is joint work with Bhargav Bhatt.

February 21  Thomas Polstra University of Utah 
A theorem about maximal CohenMacaulay modules
In this talk we will discuss a surprising uniform property concerning the class of CohenMacaulay modules over strongly Fregular rings. As an application, we show that the torsion subgroup of the divisor class group of a local strongly Fregular ring is finite.

February 28  Gregory Taylor University of Illinois at Chicago 
Inversion of adjunction for Fsignature
Strongly Fregular 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 Fregular inversion of adjunction via the Fsignature.

March 4, **Wednesday** LCB 323  Florian Enescu Georgia State University 

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