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arXiv · 2012.04013

Relative Fontaine-Messing theory over power series rings

Tong Liu·Yong Suk Moon·Deepam Patel
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Abstract

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 \'etale cohomology in this setting.

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Tong Liu, Yong Suk Moon, Deepam Patel. 2020-12-07. Relative Fontaine-Messing theory over power series rings. https://doi.org/10.1093/imrn/rnad247

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