On the Hilbert eigenvariety at exotic and CM classical weight 1 points
Abstract Let F be a totally real number field and let f be a classical cuspidal p-regular Hilbert modular eigenform over F of parallel weight 1. Let x be the point on the p-adic Hilbert eigenvariety $${\mathcal...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/136894 |
| _version_ | 1811090386100158464 |
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| author | Betina, Adel Deo, Shaunak V. Fité, Francesc |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Betina, Adel Deo, Shaunak V. Fité, Francesc |
| author_sort | Betina, Adel |
| collection | MIT |
| description | Abstract
Let F be a totally real number field and let f be a classical cuspidal p-regular Hilbert modular eigenform over F of parallel weight 1. Let x be the point on the p-adic Hilbert eigenvariety
$${\mathcal {E}}$$
E
corresponding to an ordinary p-stabilization of f. We show that if the p-adic Schanuel conjecture is true, then
$${\mathcal {E}}$$
E
is smooth at x if f has CM. If we additionally assume that
$$F/\mathbb {Q}$$
F
/
Q
is Galois, we show that the weight map is étale at x if f has either CM or exotic projective image (which is the case for almost all cuspidal Hilbert modular eigenforms of parallel weight 1). We prove these results by showing that the completed local ring of the eigenvariety at x is isomorphic to a universal nearly ordinary Galois deformation ring. |
| first_indexed | 2024-09-23T14:44:47Z |
| format | Article |
| id | mit-1721.1/136894 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:44:47Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1368942023-03-15T19:14:53Z On the Hilbert eigenvariety at exotic and CM classical weight 1 points Betina, Adel Deo, Shaunak V. Fité, Francesc Massachusetts Institute of Technology. Department of Mathematics Abstract Let F be a totally real number field and let f be a classical cuspidal p-regular Hilbert modular eigenform over F of parallel weight 1. Let x be the point on the p-adic Hilbert eigenvariety $${\mathcal {E}}$$ E corresponding to an ordinary p-stabilization of f. We show that if the p-adic Schanuel conjecture is true, then $${\mathcal {E}}$$ E is smooth at x if f has CM. If we additionally assume that $$F/\mathbb {Q}$$ F / Q is Galois, we show that the weight map is étale at x if f has either CM or exotic projective image (which is the case for almost all cuspidal Hilbert modular eigenforms of parallel weight 1). We prove these results by showing that the completed local ring of the eigenvariety at x is isomorphic to a universal nearly ordinary Galois deformation ring. 2021-11-01T14:34:02Z 2021-11-01T14:34:02Z 2020-10-31 2021-07-06T03:26:36Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136894 en https://doi.org/10.1007/s00209-020-02626-1 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Betina, Adel Deo, Shaunak V. Fité, Francesc On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title | On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title_full | On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title_fullStr | On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title_full_unstemmed | On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title_short | On the Hilbert eigenvariety at exotic and CM classical weight 1 points |
| title_sort | on the hilbert eigenvariety at exotic and cm classical weight 1 points |
| url | https://hdl.handle.net/1721.1/136894 |
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