Volume 24, issue 6 (2020)

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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