论文标题
在低分支中形式方案的积分P-Adic Hodge理论
Integral p-adic Hodge theory of formal schemes in low ramification
论文作者
论文摘要
我们证明，对于任何合适的平稳形式方案$ \ frak x $ over $ \ mathcal o_k $，其中$ \ mathcal o_k $是整数是整数的戒指。当$ IE <p-1 $时，专业化承认不错的分解。多亏了Bhatt，Morrow和Scholze最近的作品中的比较定理，当同居学度$ i $满足$ IE <P-1 $时，我们可以获得正式方案的整体比较定理，该$ ie <p-1 $概述了在Fontaine-Mess和Caruso和Caruso的情况下$（i+1）E <P-1 $ Prove $（i+1）E <p-1 $。
We prove that for any proper smooth formal scheme $\frak X$ over $\mathcal O_K$, where $\mathcal O_K$ is the ring of integers in a complete discretely valued nonarchimedean extension $K$ of $\mathbb Q_p$ with perfect residue field $k$ and ramification degree $e$, the $i$-th Breuil-Kisin cohomology group and its Hodge-Tate specialization admit nice decompositions when $ie<p-1$. Thanks to the comparison theorems in the recent works of Bhatt, Morrow and Scholze, we can then get an integral comparison theorem for formal schemes when the cohomological degree $i$ satisfies $ie<p-1$, which generalizes the case of schemes under the condition $(i+1)e<p-1$ proven by Fontaine-Messing and Caruso.
