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