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Commutative Algebra Seminar

Singularities in mixed characteristic
Thursday, March 26, 2020
3:00-4:00 PM
1866EH East Hall Map
We discuss recent work on singularities and birational geometry in mixed characteristic. We introduce mixed characteristic versions of klt/plt singularities and multiplier/adjoint ideals, prove their analogous properties, and compare them with the existing equal characteristic singularities. The theory relies on Andre and Gabber's recent work on the existence of weakly functorial perfectoid big Cohen--Macaulay algebras that factor through the absolute integral closure. We then discuss applications, which include a uniform version of the Briancon-Skoda theorem and a klt/plt adjunction for threefolds in mixed characteristic. This talk is based on joint work in progress with Karl Schwede, Kevin Tucker, Joe Waldron and Jakub Witaszek. Speaker(s): Linquan Ma (Purdue University)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics