论文标题
低维和分支中的整体P-Adic Hodge过滤
Integral p-adic Hodge filtrations in low dimension and ramification
论文作者
论文摘要
考虑到一个积分的P-ADIC品种，我们观察到，如果积分hodge--de rham光谱序列表现良好，那么特殊的纤维就会知道通用纤维的hodge数量。采用整体Padic Hodge理论的最新进步，我们表明，如果可以将P-Adic品种提升为第二个Witt向量的类似物，并满足了维度和冲突索引，则可以保证这种不错的行为。这是由于deligne和fontaine而引起的（分支）的混合特征类似物。最后，我们讨论了一个示例，说明了上述提升条件的必要性，这是独立关注的。
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 and Fontaine--Messing. Lastly, we discuss an example illustrating the necessity of the aforementioned lifting condition, which is of independent interest.
