Kaledin's degeneration theorem and topological Hochschild homology

TL;DR

This paper provides a concise proof of Kaledin's degeneration theorem using topological Hochschild homology and cyclotomic spectra, extending the results to relative cases in various characteristics.

Contribution

It offers a new, streamlined proof of Kaledin's theorem and extends the degeneration results to relative settings in characteristic zero and p.

Findings

Proof of Kaledin's degeneration theorem using topological Hochschild homology

Extension of the degeneration theorem to relative cases in different characteristics

Application of cyclotomic spectra theory in noncommutative Hodge theory

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 $p$.