On the levels of mod \(l\) Hilbert modular forms (Q2755156)
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scientific article; zbMATH DE number 1669674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the levels of mod \(l\) Hilbert modular forms |
scientific article; zbMATH DE number 1669674 |
Statements
8 November 2001
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levels of modular Galois representations
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raising the levels of Hilbert modular forms
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level lowering
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Shimura curves
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On the levels of mod \(l\) Hilbert modular forms (English)
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The author proves a Hilbert modular analogue of a theorem of \textit{K. Ribet} [Invent. Math. 100, 431-476 (1990; Zbl 0773.11039)] on lowering the levels of modular \(\bmod \ell\) Galois representations. This complements an earlier work of \textit{F. Jarvis} [Math. Ann. 313, 141-160 (1999; Zbl 0978.11020)] on level lowering theorems in the totally real case and could be combined with totally real versions of the Taylor-Wiles method to study deformation spaces of Galois representations of totally real fields and the relevant modularity conjectures. The proof is based on working with integral models of certain Shimura curves, and he also proves a theorem for raising the levels of \(\bmod \ell\) Hilbert modular forms.
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