$(φ,Γ)$-modules over relatively discrete algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917228863029248 |
|---|---|
| author | Mikami, Yutaro |
| author_facet | Mikami, Yutaro |
| contents | In this paper, we study $(φ,Γ)$-modules over rings which are "combinations of discrete algebras and affinoid $\mathbb{Q}_p$-algebras", and prove basic results such as the existence of a fully faithful functor from the category of Galois representations, the deperfection of $(φ,Γ)$-modules over perfect period rings, and the dualizability of the cohomology of $(φ,Γ)$-modules, and the classification of $(φ,Γ)$-modules of rank $1$. This work is motivated by the categorical $p$-adic Langlands correspondence for locally analytic representations, as proposed by Emerton-Gee-Hellmann, and the $GL_1$ case, as formulated and proved by Rodrigues Jacinto-Rodríguez Camargo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $(φ,Γ)$-modules over relatively discrete algebras Mikami, Yutaro Number Theory Algebraic Geometry In this paper, we study $(φ,Γ)$-modules over rings which are "combinations of discrete algebras and affinoid $\mathbb{Q}_p$-algebras", and prove basic results such as the existence of a fully faithful functor from the category of Galois representations, the deperfection of $(φ,Γ)$-modules over perfect period rings, and the dualizability of the cohomology of $(φ,Γ)$-modules, and the classification of $(φ,Γ)$-modules of rank $1$. This work is motivated by the categorical $p$-adic Langlands correspondence for locally analytic representations, as proposed by Emerton-Gee-Hellmann, and the $GL_1$ case, as formulated and proved by Rodrigues Jacinto-Rodríguez Camargo. |
| title | $(φ,Γ)$-modules over relatively discrete algebras |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2409.14145 |