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SUMMARY:Kevin Tucker (University of Illinois at Chicago)
DTSTART:20210401T203000Z
DTEND:20210401T220000Z
DTSTAMP:20260423T021435Z
UID:FOTR/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/44/">Gl
 obal +- regularity</a>\nby Kevin Tucker (University of Illinois at Chicago
 ) as part of Fellowship of the Ring\n\n\nAbstract\nOver a field of charact
 eristic $p > 0$\, a globally F-regular algebraic variety is a special type
  of Frobenius split variety. They are necessarily locally (strongly) F-reg
 ular\, hence normal and Cohen-Macaulay\, but also satisfy a number of part
 icularly nice global properties as well. A smooth projective variety is gl
 obally F-regular if its (normalized) coordinate rings are F-regular\, a co
 ndition which imposes strong positivity properties and implies Kodaira-typ
 e vanishing results. Globally F-regular varieties are closely related to c
 omplex log Fano varieties via reduction to characteristic $p > 0$.\n\nIn t
 his talk\, I will describe an analog of global F-regularity in the mixed c
 haracteristic setting called global +-regularity and introduce certain sta
 ble sections of adjoint line bundles. This is inspired by recent work of B
 hatt 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\, Z
 solt Patakfalvi\, Karl Schwede\, Joe Waldron\, and Jakub Witaszek.\n
LOCATION:https://researchseminars.org/talk/FOTR/44/
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