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.

v2: 29 pages, minor updates, comments still welcome