EVENT DETAILS AND ABSTRACT

Title: Derived de Rham complex in p-adic analytic geometry
Speaker: Haoyang Guo
Speaker Info: MPIM
Brief Description:
Special Note:
Abstract:

For a smooth complex algebraic variety, a well-known result of Grothendieck states that cohomology of algebraic de Rham complex is naturally isomorphic to complex-valued singular cohomology. When the variety is not smooth, this isomorphism often fails, and one of the remedies is to replace the former by derived de Rham complex, which is constructed using homotopy theory. In this talk, we consider the analogue of derived de Rham complex in p-adic analytic geometry. We show that the obtained cohomology theory behaves very well for proper rigid analytic spaces. Moreover, jointly with Shizhang Li, we extend the construction to perfectoid spaces, and recover the period sheaves of Brinon and Scholze in rational p-adic Hodge theory.