Multivariable de Rham representations, Sen theory, an $p$-adic differential operators
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRINON, O | |
| hal.structure.identifier | Dipartimento di Matematica [Padova] | |
| dc.contributor.author | CHIARELLOTTO, B | |
| hal.structure.identifier | Dipartimento di Matematica [Padova] | |
| dc.contributor.author | MAZZARI, N | |
| dc.date.accessioned | 2024-04-04T02:43:55Z | |
| dc.date.available | 2024-04-04T02:43:55Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191366 | |
| dc.description.abstractEn | Let $K$ be a complete discretely valued field extension of $\mathbf{Q}_p$ with perfect residue field. We consider $p$-adic representations of a finite product $G_{K,\Delta}=G_K^{\Delta}$ of the absolute Galois group $G_K$ of $K$. This product appears as the fundamental group of a product of diamonds. We develop the corresponding $p$-adic Hodge theory by constructing analogues of the classical period rings $\mathsf{B}_{\text{dR}}$ and $\textsf{B}_{\text{HT}}$, and multivariable Sen theory. In particular, we associate to any $p$-adic representation $V$ of $G_{K,\Delta}$ an integrable $p$-adic differential system in several variables $\text{D}_{\text{dif}}(V)$. We prove that this system is trivial if and only if the representation $V$ is de Rham. Finally, we relate this differential system to the multivariable overconvergent $(\varphi,\Gamma)$-module of $V$ constructed by Pal and Zábrádi, along classical Berger's construction. | |
| dc.language.iso | en | |
| dc.title.en | Multivariable de Rham representations, Sen theory, an $p$-adic differential operators | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03441978 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03441978v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BRINON,%20O&CHIARELLOTTO,%20B&MAZZARI,%20N&rft.genre=preprint |
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