Modularity of certain potentially Barsotti-Tate Galois representations

DOI10.1090/S0894-0347-99-00287-8zbMath0923.11085WikidataQ55892254 ScholiaQ55892254MaRDI QIDQ4235731

Brian Conrad, Fred Diamond, Richard Taylor

Publication date: 22 March 1999

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

elliptic curveGalois representationmodular formsGalois representationsuniversal deformationHecke algebramodular curves.

Mathematics Subject Classification ID

Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18)

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Uses Software

• ecdata

Cites Work

• On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
• Sur les représentations galoisiennes modulo \(\ell\) attachées aux formes modulaires. (On Galois representations modulo \(\ell\) attached to modular forms)
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Non-optimal levels of \(\text{mod }l\) modular representations
• Lifting modular mod \(l\) representations
• The Taylor-Wiles construction and multiplicity one
• Modular forms and \(p\)-adic Hodge theory
• The weight in Serre's conjectures on modular forms
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• On deformation rings and Hecke rings
• Ramified deformation problems
• Some consequences of the Riemann hypothesis for varieties over finite fields
• Good reduction of abelian varieties
• Algebraic number fields and symplectic discontinuous groups
• Galois properties of points of finite order of elliptic curves
• Le problème des groupes de congruence pour \(SL_2\)
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Néron Models
• Schémas en groupes de type $(p,\ldots,p)$
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
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