## Derived Alegbraic Geometry seminar: Topological Hochschild homology and Witt vectors

Seminar | April 27 | 1-2 p.m. | 891 Evans Hall

Martin Speirs, University of Copenhagen

Department of Mathematics

Topological Hochschild homology (THH) is a homology theory for (derived) rings which has had several applications to algebraic K-theory and, more recently, to integral p-adic Hodge theory. I will introduce THH($A$) for a ring $A$ and discuss its relation to the (p-typical) Witt vectors of $A$, establishing (certain fixed points of) THH as a derived Witt vector construction. This is the beginning of a story which provides a link between topological Hochschild homology and crystalline cohomology from algebraic geometry in a manner very similar to the classical Hochschild-Kostant-Rosenberg theorem.

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