A remark on potentially semi-stable representations of Hodge-Tate type (0,1)
In this note we complement a part of a theorem of Fontaine-Mazur. We show that if $(V,\rho)$ is an irreducible finite dimensional representation of the Galois group $Gal({\bar K}/K)$ of a finite extension of $K\Q_p$, of Hodge-Tate type $(0,1)$ then it is potentially semi-stable if and only if it is...
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| Format: | Journal article |
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Springer-Verlag
2002
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| _version_ | 1826258263111368704 |
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| author | Joshi, K Kim, M |
| author_facet | Joshi, K Kim, M |
| author_sort | Joshi, K |
| collection | OXFORD |
| description | In this note we complement a part of a theorem of Fontaine-Mazur. We show that if $(V,\rho)$ is an irreducible finite dimensional representation of the Galois group $Gal({\bar K}/K)$ of a finite extension of $K\Q_p$, of Hodge-Tate type $(0,1)$ then it is potentially semi-stable if and only if it is potentially crystalline. This was proved by Fontaine-Mazur for dimension two and $p\geq 5$ by their classfication theorem. |
| first_indexed | 2024-03-06T18:31:11Z |
| format | Journal article |
| id | oxford-uuid:09b4f130-4444-455c-9047-e8bbc5ddc920 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:31:11Z |
| publishDate | 2002 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:09b4f130-4444-455c-9047-e8bbc5ddc9202022-03-26T09:19:47ZA remark on potentially semi-stable representations of Hodge-Tate type (0,1)Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:09b4f130-4444-455c-9047-e8bbc5ddc920Symplectic Elements at OxfordSpringer-Verlag2002Joshi, KKim, MIn this note we complement a part of a theorem of Fontaine-Mazur. We show that if $(V,\rho)$ is an irreducible finite dimensional representation of the Galois group $Gal({\bar K}/K)$ of a finite extension of $K\Q_p$, of Hodge-Tate type $(0,1)$ then it is potentially semi-stable if and only if it is potentially crystalline. This was proved by Fontaine-Mazur for dimension two and $p\geq 5$ by their classfication theorem. |
| spellingShingle | Joshi, K Kim, M A remark on potentially semi-stable representations of Hodge-Tate type (0,1) |
| title | A remark on potentially semi-stable representations of Hodge-Tate type
(0,1) |
| title_full | A remark on potentially semi-stable representations of Hodge-Tate type
(0,1) |
| title_fullStr | A remark on potentially semi-stable representations of Hodge-Tate type
(0,1) |
| title_full_unstemmed | A remark on potentially semi-stable representations of Hodge-Tate type
(0,1) |
| title_short | A remark on potentially semi-stable representations of Hodge-Tate type
(0,1) |
| title_sort | remark on potentially semi stable representations of hodge tate type 0 1 |
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