Algebraic Geometry Seminar

Grothendieck--Serre for isotropic groups

Speaker: Kęstutis Česnavičius, Université Paris-Saclay, Orsay; IAS

Location: Warren Weaver Hall 512

Date: Tuesday, October 24, 2023, 3:30 p.m.


The Grothendieck–Serre conjecture predicts that every generically trivial torsor under
a reductive group G over a regular semilocal ring R is trivial. We establish this for unramified R
granted that G is totally isotropic, that is, has a “maximally transversal” parabolic R-subgroup. We
also use purity for the Brauer group to reduce the conjecture for unramified R to simply connected
G—a much less direct such reduction of Panin had been a step in solving the equal characteristic case
of Grothendieck–Serre. The talk is based on joint work with Roman Fedorov.