Seminar
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| Location: | SLMath: Online/Virtual |
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.
Abstract:
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.
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