Kaledin's degeneration theorem and topological Hochschild homology

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 $p$.

23 pages, revised version to appear in Geometry and Topology

References in corpus (9)

• Nilpotence and descent in equivariant stable homotopy theory
• On Serre duality for compact homologically smooth DG algebras
• Topological Hochschild homology and integral $p$-adic Hodge theory
• Topological Hochschild homology and the Hasse-Weil zeta function
• Periodic cyclic homology and derived de Rham cohomology
• The geometry of the cyclotomic trace
• Homotopy theory of Spectral categories
• Spectral sequences for cyclic homology
• The strong Künneth theorem for topological periodic cyclic homology

Cited by in corpus (7)

• Counterexamples to Hochschild--Kostant--Rosenberg in characteristic $p$
• Unwinding the relative Tate diagonal
• On the periodic topological cyclic homology of DG categories in characteristic p
• Bokstedt periodicity generator via K-theory
• An operadic proof of the BTT Theorem
• Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$
• Spectral algebras and non-commutative Hodge-to-de Rham degeneration