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arXiv · 2507.21801

On a characterisation of perfectoid fields by Iwasawa theory

Gautier Ponsinet
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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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Gautier Ponsinet. 2025-07-29. On a characterisation of perfectoid fields by Iwasawa theory. https://arxiv.org/abs/2507.21801

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