Multivariable $p$-adic Hodge theory for products of Galois groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916619046879232 |
|---|---|
| author | Poyeton, Léo Vanni, Pietro |
| author_facet | Poyeton, Léo Vanni, Pietro |
| contents | In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(φ,Γ)$-modules, generalizing results from Pal-Zabradi and Carter-Kedlaya-Zabradi, using Colmez-Sen-Tate descent. We also define rings of multivariable crystalline and semistable periods, and explain how to recover this multivariable $p$-adic theory attached to a family of representations from its multivariable $(φ,Γ)$-module. We also explain how our framework allows us to recover the main results of Brinon-Chiarellotto-Mazzari on multivariable $p$-adic Galois representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariable $p$-adic Hodge theory for products of Galois groups Poyeton, Léo Vanni, Pietro Number Theory 11S20, 11F85, 13J10, 46S10 In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(φ,Γ)$-modules, generalizing results from Pal-Zabradi and Carter-Kedlaya-Zabradi, using Colmez-Sen-Tate descent. We also define rings of multivariable crystalline and semistable periods, and explain how to recover this multivariable $p$-adic theory attached to a family of representations from its multivariable $(φ,Γ)$-module. We also explain how our framework allows us to recover the main results of Brinon-Chiarellotto-Mazzari on multivariable $p$-adic Galois representations. |
| title | Multivariable $p$-adic Hodge theory for products of Galois groups |
| topic | Number Theory 11S20, 11F85, 13J10, 46S10 |
| url | https://arxiv.org/abs/2502.12341 |