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Kaledin's degeneration theorem and topological Hochschild homology

Akhil Mathew

Geometry & Topology 24 (2020) 2675–2708
DOI: 10.2140/gt.2020.24.2675
Abstract

We give a short proof of Kaledin’s theorem on the degeneration of the noncommutative Hodge-to-de Rham spectral sequence. Our approach is based on topological Hochschild homology and the theory of cyclotomic spectra. As a consequence, we also obtain relative versions of the degeneration theorem, both in characteristic zero and for regular bases in characteristic p.

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Keywords
topological Hochschild homology, Hodge-to-de Rham spectral sequence, differential graded categories
Mathematical Subject Classification 2010
Primary: 16E40, 55P43
Secondary: 14A22
References
Publication
Received: 16 November 2017
Revised: 18 June 2019
Accepted: 15 December 2019
Published: 29 December 2020
Proposed: Stefan Schwede
Seconded: Ulrike Tillmann, Jesper Grodal
Authors
Akhil Mathew
Department of Mathematics
University of Chicago
Chicago, IL
United States