The Witt vectors for Green functors
Andrew J. Blumberg, Teena Gerhardt, Michael A. Hill, Tyler Lawson
TL;DR
This paper introduces a new algebraic construction of Witt vectors for Green functors via twisted Hochschild homology, connecting algebraic and topological invariants, and extending existing theories to new contexts.
Contribution
It defines twisted Hochschild homology for Green functors and interprets it as Witt vectors, extending Hesselholt's construction to a broader algebraic setting.
Findings
Provides a new algebraic invariant for Green functors.
Connects twisted Hochschild homology with the $E_2$ term of the K"unneth spectral sequence.
Extends Witt vector theory to noncommutative and Green functor contexts.
Abstract
We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology , and it describes the term of the K\"unneth spectral sequence for relative . Applied to ordinary rings, we obtain new algebraic invariants. Extending Hesselholt's construction of the Witt vectors of noncommutative rings, we interpret our construction as providing Witt vectors for Green functors.
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