THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$
Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$. As a consequence, we establish (under the usual Ta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2015-02-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508615000013/type/journal_article |
| _version_ | 1811156256994361344 |
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| author | TOBY GEE TONG LIU DAVID SAVITT |
| author_facet | TOBY GEE TONG LIU DAVID SAVITT |
| author_sort | TOBY GEE |
| collection | DOAJ |
| description | Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$. As a consequence, we establish (under the usual Taylor–Wiles hypothesis) the weight part of Serre’s conjecture for $\text{GL}(2)$ over arbitrary totally real fields. |
| first_indexed | 2024-04-10T04:48:37Z |
| format | Article |
| id | doaj.art-c0b66f88faa5471f88ac14c92f3ee319 |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:48:37Z |
| publishDate | 2015-02-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-c0b66f88faa5471f88ac14c92f3ee3192023-03-09T12:34:22ZengCambridge University PressForum of Mathematics, Pi2050-50862015-02-01310.1017/fmp.2015.1THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$TOBY GEE0TONG LIU1DAVID SAVITT2Department of Mathematics, Imperial College London SW7 2RH, UK;Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA;Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$. As a consequence, we establish (under the usual Taylor–Wiles hypothesis) the weight part of Serre’s conjecture for $\text{GL}(2)$ over arbitrary totally real fields.https://www.cambridge.org/core/product/identifier/S2050508615000013/type/journal_article11F33 (primary)11F80 (secondary) |
| spellingShingle | TOBY GEE TONG LIU DAVID SAVITT THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ Forum of Mathematics, Pi 11F33 (primary) 11F80 (secondary) |
| title | THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ |
| title_full | THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ |
| title_fullStr | THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ |
| title_full_unstemmed | THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ |
| title_short | THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$ |
| title_sort | weight part of serre s conjecture for text gl 2 |
| topic | 11F33 (primary) 11F80 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050508615000013/type/journal_article |
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