The Emerton--Gee stack of rank one $(φ,Γ)$-modules
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917829696028672 |
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| author | Pham, Dat |
| author_facet | Pham, Dat |
| contents | We give a classification of rank one $(φ,Γ)$-modules with coefficients in a $p$-adically complete $\mathbf{Z}_p$-algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in {arXiv:1908.07185}, which gives an explicit description of the Emerton--Gee stack of $(φ,Γ)$-modules in the rank one case. In fact, our method also applies in the context of rank one \' etale $φ$-modules (i.e. in the absence of a $Γ$-action), generalizing another result of Emerton--Gee. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02888 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Emerton--Gee stack of rank one $(φ,Γ)$-modules Pham, Dat Number Theory We give a classification of rank one $(φ,Γ)$-modules with coefficients in a $p$-adically complete $\mathbf{Z}_p$-algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in {arXiv:1908.07185}, which gives an explicit description of the Emerton--Gee stack of $(φ,Γ)$-modules in the rank one case. In fact, our method also applies in the context of rank one \' etale $φ$-modules (i.e. in the absence of a $Γ$-action), generalizing another result of Emerton--Gee. |
| title | The Emerton--Gee stack of rank one $(φ,Γ)$-modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2206.02888 |