Time: 9h00, 7/5/2014

Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: Based on our recent work with ND Duong, we try to understand the structure of flat affine group schemes over a Dedekind ring. It is well-known that, over a field, an affine group is a limit of an inverse system of group schemes of finite type, in which all the structure maps are onto (faithfully flat). This is no more true for group schemes over a Dedekind ring, even if the group scheme is flat. In our recent work, we show that a flat group scheme over a Dedekind ring can be represented as the limit of a, so to say, double inverse system, on one slice of which the structure maps are faithfully flat and on the other slice the structure maps are Neron's blow-up. Some applications to the differential fundamental group scheme of a relative scheme is also discussed. This is a work in progress with dos Santos and Nguyen Dai Duong.