论文标题
相对fontaine-messing理论与力量系列戒指
Relative Fontaine-Messing theory over power series rings
论文作者
论文摘要
让$ k $是特征$ p> 2 $，$ r：= w（k）[\！[\！[t_1，\ dots，t_d] \！] $是witt载体上的电源系列戒指，而$ x $是$ r $上的平滑适当方案。本文的主要目的是将古典Fontaine-Messing理论扩展到基本环为$ r $的环境。特别是，在这种情况下，我们获得了$ x/r $ $ x/r $的扭转晶体共同体和扭转典型的比较定理。
Let $k$ be a perfect field of characteristic $p>2$, $R := W(k)[\![t_1, \dots, t_d]\!]$ be the power series ring over the Witt vectors, and $X$ be a smooth proper scheme over $R$. The main goal of this article is to extend classical Fontaine-Messing theory to the setting where the base ring is $R$. In particular, we obtain comparison theorems between torsion crystalline cohomology of $X/R$ and torsion étale cohomology in this setting.
