de Rham K(pi,1)-schemes

Thời gian: 16h45-18h00, thứ Năm, 29/10

Địa điểm: Phòng 512 nhà A6, Viện toán học

Abstract: Motivated by the work of Esnault–Hai, one has the notion of de Rham $K(\pi,1)$ schemes, defined as follows. Given a smooth, proper, geometrically connected scheme X over a field k of characteristic 0 and a base point $x \inX(k)$, one can define its differential fundamental group π^diff(X/k), which arises from the Tannakian duality of the category of coherent integrable connections on X. Using the formalism of $δ\delta$-functors, one can define natural morphisms between the group scheme cohomology of π^diff(X/k) and the de Rham cohomology of X. One says that X with base point $x \inX(k)$ is de Rham $K(\pi,1)$ if these morphisms are all isomorphisms.

In this talk, I will discuss some examples of de Rham $K(\pi,1)$ schemes and related questions. This talk is based on joint work with Nguyen Quang Khai, Phung Ho Hai, and Dao Van Thinh, as well as work in progress with Hélène Esnault.