# Emanuele Dotto: Witt vectors with coefficients and the components of the Hill-Hopkins-Ravenel norm

**Time: **
Tue 2019-04-30 13.15 - 15.00

**Location: **
Room 35, House 5, Kräftriket campus, Stockholm University

**Participating: **
Emanuele Dotto (Bonn)

ABSTRACT: The first part of the talk will review the relationship between the Witt vectors of a commutative ring and its topological Hochschild homology spectrum, established by Hesselholt and Madsen. The second part will focus on recent work with Krause, Patchkoria and Nikolaus which constructs the Witt vectors of a ring with coefficients in a bimodule. This construction extends Kaledin's "polynomial Witt vectors" of perfect fields and Hesselholt's Witt vectors of non-commutative rings. I will explain how to use our framework to extend the characteristic polynomial to endomorphisms of finitely generated projective modules over non-commutative rings, and how to calculate the components of the Hill-Hopkins-Ravenel norm for finite cyclic groups.