Base change and a problem of Serre

DOI10.1215/S0012-7094-01-10712-6zbMath1016.11017OpenAlexW2066237927MaRDI QIDQ1847810

Christopher M. Skinner, Andrew Wiles

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10712-6

zbMATH Keywords

Hilbert modular formsbase changemodularityquaternion algebraGalois-representation

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80)

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Cites Work

• On Galois representations associated to Hilbert modular forms
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• On ordinary \(\lambda\)-adic representations associated to modular forms
• Level lowering for modular \(\text{mod }\ell\) representations over totally real fields
• Residually reducible representations and modular forms
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• Modular elliptic curves and Fermat's Last Theorem
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
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