Correspondences on Shimura curves and Mazur's principle at \(p\) (Q1884534)
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scientific article; zbMATH DE number 2113416
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Correspondences on Shimura curves and Mazur's principle at \(p\) |
scientific article; zbMATH DE number 2113416 |
Statements
Correspondences on Shimura curves and Mazur's principle at \(p\) (English)
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1 November 2004
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The author extends his earlier result [\textit{F. Jarvis}, Compos. Math. 116, No. 1, 39--79 (1999; Zbl 1053.11043)] concerning Mazur's Principle for totally real number fields to the case of primes as in [\textit{K. A. Ribet}, Invent. Math. 100, 431--476 (1990; Zbl 0773.11039)]. As an application, he deduces an analogue of Fermat's Last Theorem over certain totally real number fields from the modularity of semistable elliptic curves (Theorem 8.1).
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Mazur's principle
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Galois representation
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Hilbert eigenform
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Shimura curve
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Hecke algebra
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