Integral \(p\)-adic Hodge filtrations in low dimension and ramification
Summary: 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.
scientific article; zbMATH DE number 7608242
scientific article