The Geometry of Hida Families II: $\Lambda$-adic $(\varphi,\Gamma)$-modules and $\Lambda$-adic Hodge Theory
Abstract
We construct the -adic crystalline and Dieudonn\'e analogues of Hida's ordinary -adic \'etale cohomology, and employ integral -adic Hodge theory to prove -adic comparison isomorphisms between these cohomologies and the -adic de Rham cohomology studied in the prequel to this paper as well as Hida's -adic \'etale cohomology. As applications of our work, we provide a "cohomological" construction of the family of -modules attached to Hida's ordinary -adic \'etale cohomology by the work of Dee, and we give a new and purely geometric proof of Hida's finitenes and control theorems. We also prove suitable -adic duality theorems for each of the cohomologies we construct.
Cite
@article{arxiv.1407.5709,
title = {The Geometry of Hida Families II: $\Lambda$-adic $(\varphi,\Gamma)$-modules and $\Lambda$-adic Hodge Theory},
author = {Bryden Cais},
journal= {arXiv preprint arXiv:1407.5709},
year = {2019}
}
Comments
This paper is a continuation of our previous paper "The Geometry of Hida Families I: $\Lambda$-adic de Rham cohomology", and is a revised version of part of the paper arXiv:1209.0046