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arXiv · 2503.14041

A pro-\'etale-to-de Rham comparison theorem for curves

Sally Gilles
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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)].

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Sally Gilles. 2025-03-18. A pro-\'etale-to-de Rham comparison theorem for curves. https://arxiv.org/abs/2503.14041

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