Student Arithmetic Geometry Seminar: Kaledin's degeneration theorem and THH (CANCELLED, will be rescheduled)
Seminar | October 11 | 4:10-5 p.m. | 891 Evans Hall
Martin Speirs, UC Berkeley
THIS WEEK'S SEMINAR HAS BEEN CANCELLED DUE TO POWER OUTAGE.
This talk is concerned with an application of topological Hochschild homology (THH) to give a new proof of a result originally due to Kaledin. Given a variety smooth and proper over a field of characteristic zero, Deligne and Illusie (1987) provided a purely algebraic proof of a (non-canonical) decomposition of the de Rham cohomology into a sum of Hodge cohomology groups. In 2008 Kaledin proved a non-commutative version of the Deligne-Illusie result. Namely, he proved that for a differential graded category smooth and proper over a field of characteristic zero, the periodic cyclic homology (which replaces de Rham cohomology) has a non-canonical splitting in terms of Hochschild homology (replacing Hodge cohomology). Recently, Akhil Mathew gave a new proof of Kaledin's theorem using THH. In my talk I will give an introduction to the ingredients in Kaledin's theorem, and sketch Mathew's proof.