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Hochschild homology for Green functors

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HHHW02 - Equivariant and motivic homotopy theory

Hochschild homology of a ring has a topological analogue for ring spectra, topological Hochschild homology (THH), which plays an essential role in the trace method approach to algebraic K-theory. For a C_n-equivariant ring spectrum, one can define C_n-relative THH . This leads to the question: What is the algebraic analogue of C_n-relative THH ? In this talk, I will define twisted Hochschild homology for Green functors, which allows us to describe this algebraic analogue. This also leads to a theory of Witt vectors for Green functors, as well as an algebraic analogue of TR-theory. This is joint work with Andrew Blumberg, Mike Hill, and Tyler Lawson.

This talk is part of the Isaac Newton Institute Seminar Series series.

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