Grothendieck-Serre and Purity of torsors

Thời gian: 16h30 - 18h00, thứ 5 ngày 19 tháng 10.

Hình thức: Offline tại phòng 612 A6 và online qua google meet, cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1

Tóm tắt: Torsors (or principal bundles) are generalization of vector bundles and they are basic objects of geometry and physics. A long-standing conjecture proposed by Grothendieck and Serre predicts that over a regular local ring, every generically trivial torsor under a reductive group scheme is trivial. The state of the art is the equi-characteristic case proved by Panin and Fedorov-Panin, the quasi-split unramified case by Cesnavicius, and the unramified case when the group scheme is constant by Guo-Liu and Guo-Panin-Stavrova. In this talk, I will introduce the Grothendieck-Serre conjecture, discuss several geometric methods (including presentation theorems and analysis of torsors over affine line), and its relation with purity.