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- Title
Integral p-adic Hodge filtrations in low dimension and ramification.
- Authors
Shizhang Li
- Abstract
Given an integral p-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 p-adic Hodge theory, we show that such a nice behavior is guaranteed if the p-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.
- Subjects
VARIETIES (Universal algebra); HODGE theory; MATHEMATICAL bounds; CHARACTERISTIC functions; DIMENSION theory (Algebra)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2022, Vol 24, Issue 11, p3801
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1237