A pro-\'etale-to-de Rham comparison theorem for curves
Algebraic Geometry
2025-11-21 v2 Number Theory
Abstract
We state a conjecture relating de Rham cohomology of a smooth rigid analytic variety to its compactly supported pro-\'etale cohomology. We prove the conjecture in the cases where the variety is a Stein curve of dimension one or a Stein space of higher dimension with low Frobenius slopes. The proof uses computation of the Galois cohomology of the almost de Rham period ring BdR[log(t)].
Cite
@article{arxiv.2503.14041,
title = {A pro-\'etale-to-de Rham comparison theorem for curves},
author = {Sally Gilles},
journal= {arXiv preprint arXiv:2503.14041},
year = {2025}
}
Comments
Error in the proof of Lemma 2.10