On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension

2025/10/14 by Rustam Steingart, Steingart, Rustam
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2510.12533

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

Let K/E/ℚ_p be a tower of finite extensions with E Galois. We relate the category of G_K-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in E with E-G_K-B-pairs and describe crystalline and de Rham objects in explicit terms. When E is a proper extension, we give a new description of the category in terms of compatible tuples of B_e-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can serve as a replacement of the fundamental exact sequence.

Citations

• Almost C_p Galois representations and vector bundles
• p-adic Fourier Theory

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