English

Relative Fontaine-Messing theory over power series rings

Number Theory 2023-11-17 v2

Abstract

Let kk be a perfect field of characteristic p>2p>2, R:=W(k)[ ⁣[t1,,td] ⁣]R := W(k)[\![t_1, \dots, t_d]\!] be the power series ring over the Witt vectors, and XX be a smooth proper scheme over RR. The main goal of this article is to extend classical Fontaine-Messing theory to the setting where the base ring is RR. In particular, we obtain comparison theorems between torsion crystalline cohomology of X/RX/R and torsion \'etale cohomology in this setting.

Keywords

Cite

@article{arxiv.2012.04013,
  title  = {Relative Fontaine-Messing theory over power series rings},
  author = {Tong Liu and Yong Suk Moon and Deepam Patel},
  journal= {arXiv preprint arXiv:2012.04013},
  year   = {2023}
}