Universal norms and the Fargues-Fontaine curve

2020/10/05 by Gautier Ponsinet, Ponsinet, Gautier
Computer Science · Mathematics · #11F85 #11S25 #14F30 #14G45 #14H60 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Primary: 11R23 #Secondary: 11F80

paper · pdf · doi:10.48550/arxiv.2010.02292

openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the module of universal norms associated with a de Rham p-adic Galois representation in a perfectoid field extension. In particular, we compute precisely this module when the Hodge-Tate weights of a representation are greater than or equal to 0. This generalises a result by Coates and Greenberg for Abelian varieties, and partially answers a question of theirs. Our method relies on the classification of vector bundles over the Fargues-Fontaine curve.

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