Galois representations of octahedral type and 2-coverings of elliptic curves.
Pilar Bayer, Gerhard Frey (1991)
Mathematische Zeitschrift
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Displaying similar documents to “On the surjectivity of Galois representations attached to elliptic curves over number fields”
Galois representations of octahedral type and 2-coverings of elliptic curves.
Some p-adic Galois Representations for Curves in Characteristic p.
Robert C. Valentini (1986)
Mathematische Zeitschrift
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On Galois representations arising from towers of coverings of P1 ... .
Y. Ihara (1986)
Inventiones mathematicae
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On families of 9-congruent elliptic curves
Tom Fisher (2015)
Acta Arithmetica
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We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
Explicit deformation of Galois representations.
Nigel Boston (1991)
Inventiones mathematicae
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Icosahedral Galois Extensions and Elliptic Curves.
Annette Klute (1997)
Manuscripta mathematica
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Galois representations on profinite braid groups on curves.
Makoto Matsumoto (1996)
Journal für die reine und angewandte Mathematik
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Deformations of Galois representations arising from degenerate extensions
Adam Logan (2002)
Acta Arithmetica
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Galois representations of dihedral type over ℚₚ
Peder Frederiksen, Ian Kiming (2004)
Acta Arithmetica
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On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve with complex multiplication.
Kay Wingberg (1991)
Journal für die reine und angewandte Mathematik
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New forms and Galois representations of octahedral type. (Formes primitives et représentations galoisiennes de type octaédral.)
Cassou-Noguès, Philippe, Jehanne, Arnaud (1996)
Experimental Mathematics
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Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
Richard Taylor (2008)
Publications Mathématiques de l'IHÉS
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We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.
Rational points on twists of X₀(63)
Nils Bruin, Julio Fernández, Josep González, Joan-C. Lario (2007)
Acta Arithmetica
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On cohomological systems of Galois representations
Wojciech Gajda, Sebastian Petersen (2016)
Banach Center Publications
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The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead...
Elliptic curves with complex multiplication and Galois module structure.
Anupam Srivastav, Martin J. Taylor (1990)
Inventiones mathematicae
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Compatible families of elliptic type
David E. Rohrlich (2010)
Acta Arithmetica
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On the equation a³ + b³ⁿ = c²
Michael A. Bennett, Imin Chen, Sander R. Dahmen, Soroosh Yazdani (2014)
Acta Arithmetica
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We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.