A pro-étale-to-de Rham comparison theorem for curves

2025/03/18 by Gilles, Sally
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.14041

Abstract

We state a conjecture relating de Rham cohomology of a smooth rigid analytic variety to its compactly supported pro-étale 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)].

Related

• On the cohomology of p-adic analytic spaces, II: The C_{\rm st}-conjecture
• De Rham comparison and Poincaré duality for rigid varieties
• The de Rham comparison theorem for Deligne-Mumford stacks
• Rational p-adic Hodge theory for rigid-analytic varieties
• On the Kummer pro-étale cohomology of \mathbb B_dR