Universal norms of p-adic Galois representations and the Fargues-Fontaine curve

Abstract: In 1996, Coates and Greenberg computed explicitly the module of universal norms for abelian varieties over perfectoid field extensions. The computation of this module is employed in Iwasawa theory, notably to prove "control theorems" for Selmer groups, generalizing Mazur's foundational work on the Iwasawa theory of abelian varieties over Zp-extensions.

Coates and Greenberg raised the natural question on possible generalisations of their result to p-adic representations. In this talk, I will present a new approach to this question relying on the classification of vector bundles over the Fargues-Fontaine curve, which allows us to answer Coate and Greenberg's question affirmatively in new cases.

number theory

Audience: researchers in the topic

CRM-CICMA Québec Vermont Seminar Series

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