Mathematical Sciences Research Institute

Home » Fellowship of the Ring, National Seminar: Global +-regularity


Fellowship of the Ring, National Seminar: Global +-regularity April 01, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Kevin Tucker (University of Illinois at Chicago)

To attend this seminar, you must register in advance, by clicking HERE.


Global +-Regularity


To attend this seminar, you must register in advance, by clicking HERE.


Over a field of characteristic p > 0, a globally F-regular algebraic variety is a special type of Frobenius split variety. They are necessarily locally (strongly) F-regular, hence normal and Cohen-Macaulay, but also satisfy a number of particularly nice global properties as well. A smooth projective variety is globally F-regular if its (normalized) coordinate rings are F-regular, a condition which imposes strong positivity properties and implies Kodaira-type vanishing results. Globally F-regular varieties are closely related to complex log Fano varieties via reduction to characteristic p > 0.

In this talk, I will describe an analog of global F-regularity in the mixed characteristic setting called global +-regularity and introduce certain stable sections of adjoint line bundles. This is inspired by recent work of Bhatt on the Cohen-Macaulayness of the absolute integral closure, and has applications to birational geometry in mixed characteristic. This is based on arXiv:2012.15801 and is joint work with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Joe Waldron, and Jakub Witaszek.

Asset no preview Notes 4.94 MB application/pdf

Global +-Regularity