Introduction to arithmetic D-modules.

Thời gian: 10:00 đến 11:30 ngày 04/07/2018, 10:00 đến 11:30 ngày 05/07/2018, 10:00 đến 11:30 ngày 11/07/2018, 10:00 đến 11:30 ngày 12/07/2018,

Địa điểm: C2-714, VIASM

Báo cáo viên: Daniel Caro

Tóm tắt:

The purpose of these talk is to introduce to Berthelot’s theory of arithmetic D-modules. This theory gives a formalism of Grothendieck’s six operations and for instance furnishes some cohomological interpretation of Weil zeta function associated with varieties over a finite field. Let us clarify the content of the talks. We first recall Grothendieck’s construction of the sheaf of differential operators denoted by DX/S associated to a smooth morphism X → S (e.g. of algebraic varieties). Next, for some integer m, we introduce Berthelot’s sheaf of differential operators of level m and explain by comparison why it is more suited in some sense in positive characteristic. By taking some kind of weak completion, we get Berthelot’s sheaf of differential operators of infinite orders and finite level. We will give some examples of finiteness theorems over this later sheaf of rings by using direct computations.

About Speaker: Daniel Caro is Full Professor at the University of Caen Normandy since 2008. He holds a PhD from the University of Rennes (France). He is a leading expert on p-adic cohomologies over varieties in characteristic p and the theory of D-modules of Berthelot. He has published on these topics in journals including Annals of Math. and Invent. Math