Title: Rigidity, the Goodwillie regulator, and the Gauss-Manin connection over p-adic integers.
Speaker: Boris Tsygan
Speaker Info: Northwestern University
Periodic cyclic homology of associative algebras generalizes in many ways DeRham cohomology and more generally crystalline cohomology of algebraic varieties over a field of characteristic zero. Among the properties of De Rham cohomology that can be so generalized are: rigidity under infinitesimal deformations and a regulator map from relative algebraic K theory to relative cyclic homology of a nilpotent ideal (Goodwillie), and the Gauss-Manin connection (Getzler). I will explain how these results generalize to p-adic completions of cyclic complexes over p-adic integers. These generalizations develop recent results of Beilinson and Petrov-Vologodsky.Date: Monday, April 22, 2019