Unwinding the relative Tate diagonal

Tyler Lawson

doi:10.1112/topo.12195

Unwinding the relative Tate diagonal

Tyler Lawson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a spectral sequence developed by Lipshitz and Treumann, for application to Heegaard Floer theory, converges to a localized form of topological Hochschild homology with coefficients. This allows us to show that the target of this spectral sequence can be identified with Hochschild homology when the topological Hochschild homology is torsion-free as a module over (Formula presented.), parallel to results of Mathew on degeneration of the Hodge-to-de Rham spectral sequence. To carry this out, we apply work of Nikolaus–Scholze to develop a general Tate diagonal for Hochschild-like diagrams of spectra that respect a decomposition into tensor products. This allows us to discuss the extent to which there can be a Tate diagonal for relative topological Hochschild homology.

Original language	English (US)
Pages (from-to)	674-699
Number of pages	26
Journal	Journal of Topology
Volume	14
Issue number	2
DOIs	https://doi.org/10.1112/topo.12195
State	Published - Jun 2021

Bibliographical note

Funding Information:
The author would like to thank Clark Barwick, Andrew Blumberg, Teena Gerhardt, Lars Hesselholt, Michael Hill, Robert Lipshitz, Michael Mandell, Denis Nardin, Thomas Nikolaus, and David Treumann for their assistance and forbearance through this paper's long period of development, as well as the referee for detailed comments. The author would also like to thank the Max Planck Institute for Mathematics in Bonn for their hospitality and financial support while this paper was written.

Funding Information:
The author would like to thank Clark Barwick, Andrew Blumberg, Teena Gerhardt, Lars Hesselholt, Michael Hill, Robert Lipshitz, Michael Mandell, Denis Nardin, Thomas Nikolaus, and David Treumann for their assistance and forbearance through this paper's long period of development, as well as the referee for detailed comments. The author would also like to thank the Max Planck Institute for Mathematics in Bonn for their hospitality and financial support while this paper was written.

Publisher Copyright:
© 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

Keywords

13D03
55P42 (secondary)
55P43 (primary)

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Unwinding the relative Tate diagonal

Abstract

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Keywords

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