Une conjecture C_{\rm st} pour la cohomologie à support compact

2025/11/18 by Pierre Colmez, Colmez, Pierre, Sally Gilles +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2511.14675

Final version

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

Let B be the ring of analytic functions on the Fargues-Fontaine curve Y_{\rm FF}. We show that adding p-adic analogs of log p and log 2πi kills its Galois cohomology in degrees~≥ 1. The analogous result for B⁺_{\rm dR} is folklore. This makes it possible to formulate C_{\rm dR} and C_{\rm st}-type conjectures for compact support cohomology of p-adic analytic varieties.

Citations

• Rational p-adic Hodge theory for rigid-analytic varieties
• On the cohomology of p-adic analytic spaces, II: The C_{\rm st}-conjecture

Related

• On the cohomology of p-adic analytic spaces, II: The C_{\rm st}-conjecture
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• Sur la cohomologie étale de la courbe de Fargues-Fontaine
• Duality for Arithmetic p-adic Pro-étale Cohomology of Analytic Spaces
• La curva de Fargues--Fontaine: Una motivación al estudio de la teoría de representaciones de Galois p-ádicas