Counterexamples to Hochschild--Kostant--Rosenberg in characteristic $p$

Abstract

We give counterexamples to the degeneration of the HKR spectral sequence in characteristic $p$, both in the untwisted and twisted settings. We also prove that the de Rham--$\mathrm{HP}$ and crystalline--$\mathrm{TP}$ spectral sequences need not degenerate.

arXiv commentv2: 29 pages, minor updates, comments still welcome

References in corpus (7)

• Higher Topos Theory
• Brauer groups and étale cohomology in derived algebraic geometry
• Completions and derived de Rham cohomology
• On the Blumberg-Mandell Künneth theorem for TP
• Kaledin's degeneration theorem and topological Hochschild homology
• Cohomological obstruction theory for Brauer classes and the period-index problem
• Hodge cohomology on blow-ups along subvarieties

Cited by in corpus (3)

• Dieudonné Theory via Cohomology of Classifying Stacks
• Rigid-analytic varieties with projective reduction violating Hodge symmetry
• Totaro's inequality for classifying spaces