JournalsjemsOnline First6 April 2022

Integral pp-adic Hodge filtrations in low dimension and ramification

  • Shizhang Li

    University of Michigan, Ann Arbor, USA
Integral $p$-adic Hodge filtrations in low dimension and ramification cover
Download PDF

A subscription is required to access this article.

Abstract

Given an integral pp-adic variety, we observe that if the integral Hodge–de Rham spectral sequence behaves nicely, then the special fiber knows the Hodge numbers of the generic fiber. Applying recent advancements of integral pp-adic Hodge theory, we show that such a nice behavior is guaranteed if the pp-adic variety can be lifted to an analogue of second Witt vectors and satisfies some bound on dimension and ramification index. This is a (ramified) mixed characteristic analogue of results due to Deligne–Illusie, Fontaine–Messing, and Kato. Lastly, we discuss an example illustrating the necessity of the aforementioned lifting condition, which is of independent interest.

Cite this article

Shizhang Li, Integral pp-adic Hodge filtrations in low dimension and ramification. J. Eur. Math. Soc. (2022), published online first

DOI 10.4171/JEMS/1237