WEEKLY ACTIVITIES

Grothendieck--Serre in the quasi--split unramified case
Speaker: Kestutis Cesnavicius (U. Paris Sud)

Time: 15h15, Friday, April 2, 2021

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ZOOM ID：466 356 2952
Password：mcm1234

https://zoom.com.cn/j/4663562952?pwd=MytDVU9tUlg5LzFHNHRHZmFMZ0JaUT09

Session Chair: Prof. Phung Ho Hai (VAST Hanoi)

Abstract: The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified. To overcome obstacles that have so far kept the mixed characteristic case out of reach, we adapt Artin's construction of "good neighborhoods" to the setting where the base is a discrete valuation ring, build equivariant compactifications of tori over higher dimensional bases, and study the geometry of the affine Grassmannian in bad characteristics.

For general information of the AGEA seminar, please check out

https://sites.google.com/ncts.ntu.edu.tw/agea-seminar

or the mirror site

http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html

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