On a characterisation of perfectoid fields by Iwasawa theory

2025/07/29 by Ponsinet, Gautier
#11R23 (Primary) 14G45 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.21801

Abstract

We prove that the vanishing of the module of universal norms associated with a de Rham Galois representation whose Hodge-Tate weights are not all non-positive characterises the algebraic extensions of the field of p-adic numbers whose completion is a perfectoid field. We thereby generalise results by Coates and Greenberg for abelian varieties, and by Bondarko for p-divisible groups.

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