On a characterisation of perfectoid fields by Iwasawa theory
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915547962146816 |
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| author | Ponsinet, Gautier |
| author_facet | Ponsinet, Gautier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a characterisation of perfectoid fields by Iwasawa theory Ponsinet, Gautier Number Theory 11R23 (Primary) 14G45 (Secondary) 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. |
| title | On a characterisation of perfectoid fields by Iwasawa theory |
| topic | Number Theory 11R23 (Primary) 14G45 (Secondary) |
| url | https://arxiv.org/abs/2507.21801 |