A fundamental exact sequence for the differential fundamental groupoid

Thời gian: 16h30 thứ 5 ngày 9/3/2023

Địa điểm: Phòng 612 Nhà A6, Viện Toán học

Link online: https://meet.google.com/yep-kbzk-eao?pli=1&authuser=4

Tóm tắt: The differential fundamental groupoid of a scheme over fields, introduced by H.Esnault and P.H. Hai, is a generalization of the well-known étale fundamental group. This groupoid controls integrable connections in the framework of N.Katz and leads to an interesting behavior of Gauss-Manin connections and cohomology of fundamental group schemes. We prove the existence of a fundamental exact sequence over a Dedekind domain for the differential fundamental groupoid of a projective smooth scheme with geometrically connected fibers. This is my joint work with Prof. Phung Ho Hai and Tran Phan Quoc Bao.