Modularity of trianguline Galois representations
We use the theory of trianguline $(\varphi ,\Gamma )$ -modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients. The use of pseudorigid spaces lets us construct integr...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423001160/type/journal_article |
| _version_ | 1797365285825544192 |
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| author | Rebecca Bellovin |
| author_facet | Rebecca Bellovin |
| author_sort | Rebecca Bellovin |
| collection | DOAJ |
| description | We use the theory of trianguline
$(\varphi ,\Gamma )$
-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients. The use of pseudorigid spaces lets us construct integral models of the trianguline varieties of [BHS17], [Che13] after bounding the slope, and we carry out a Taylor–Wiles patching argument for families of overconvergent modular forms. This permits us to construct a patched quaternionic eigenvariety and deduce our modularity results. |
| first_indexed | 2024-03-08T16:46:56Z |
| format | Article |
| id | doaj.art-47256aa2ba6a4f2eb722fc6a39e0b253 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-08T16:46:56Z |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-47256aa2ba6a4f2eb722fc6a39e0b2532024-01-05T09:16:02ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2023.116Modularity of trianguline Galois representationsRebecca Bellovin0https://orcid.org/0000-0003-2390-3168School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, United Kingdom; E-mail:We use the theory of trianguline $(\varphi ,\Gamma )$ -modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients. The use of pseudorigid spaces lets us construct integral models of the trianguline varieties of [BHS17], [Che13] after bounding the slope, and we carry out a Taylor–Wiles patching argument for families of overconvergent modular forms. This permits us to construct a patched quaternionic eigenvariety and deduce our modularity results.https://www.cambridge.org/core/product/identifier/S2050509423001160/type/journal_article11F8011F8511F33 |
| spellingShingle | Rebecca Bellovin Modularity of trianguline Galois representations Forum of Mathematics, Sigma 11F80 11F85 11F33 |
| title | Modularity of trianguline Galois representations |
| title_full | Modularity of trianguline Galois representations |
| title_fullStr | Modularity of trianguline Galois representations |
| title_full_unstemmed | Modularity of trianguline Galois representations |
| title_short | Modularity of trianguline Galois representations |
| title_sort | modularity of trianguline galois representations |
| topic | 11F80 11F85 11F33 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423001160/type/journal_article |
| work_keys_str_mv | AT rebeccabellovin modularityoftriangulinegaloisrepresentations |