|Date: Wednesday, April 04, 2018
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology
Abstract: For a smooth proper variety over a field of characteristic zero, the Hodge-to-de Rham spectral sequence (relating the cohomology of differential forms to de Rham cohomology) is well-known to degenerate, via Hodge theory. A "noncommutative" version of this theorem has been proved by Kaledin for smooth proper dg categories over a field of characteristic zero, based on the technique of reduction mod p. I will describe a short proof of this theorem using the theory of topological Hochschild homology, which provides a canonical one-parameter deformation of Hochschild homology in characteristic p.
Speaker: Akhil Mathew
Institution: University of Chicago