Gauss-Manin connection from the Tannakian viewpoint

Thời gian: 16h30 thứ năm, ngày 13/04

Địa điểm: Pòng 612, Nhà A6.

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

Tóm tắt: In 2006, H.Esnault and P.H.Hai used the notion of a k-affine groupoid scheme acting on a k-scheme, first introduced by P. Deligne (1990), to define the differential fundamental groupoid. In this talk, we introduce the notion of the cohomology of a groupoid scheme to study the relation between the cohomology of a differential fundamental groupoid and algebraic de Rham cohomology with integrable connection coefficients. We also introduce the induction functor of the groupoid scheme which allows us to obtain new versions of some classical results like Shapiro's lemma. As an application, we prove that the Gauss-Manin connection, associated with the first de Rham cohomology for a relative connection, is induced from a representation of a groupoid scheme. These results are my joint work with Phung Ho Hai and Tran Phan Quoc Bao.