Deformations of Galois representations arising from degenerate extensions
Adam Logan (2002)
Acta Arithmetica
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Displaying similar documents to “An infinite ferm in the universal deformation space of Galois representations.”
Deformations of Galois representations arising from degenerate extensions
Explicit deformation of Galois representations.
Nigel Boston (1991)
Inventiones mathematicae
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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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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.
Modularity of Galois representations
Chris Skinner (2003)
Journal de théorie des nombres de Bordeaux
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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, -adic Galois representations associated to holomorphic Hilbert modular newforms.
Galois representations of dihedral type over ℚₚ
Peder Frederiksen, Ian Kiming (2004)
Acta Arithmetica
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On Galois representations associated to Hilbert modular forms.
Frazer Jarvis (1997)
Journal für die reine und angewandte Mathematik
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Computations of Galois representations associated to modular forms of level one
Peng Tian (2014)
Acta Arithmetica
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We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved...
On representations of the Weil group with bounded conductor.
D. Blasius, G. Anderson, G. Zettler (1994)
Forum mathematicum
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On Galois representations associated to Hilbert modular forms.
Richard Taylor (1989)
Inventiones mathematicae
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On Galois representations arising from towers of coverings of P1 ... .
Y. Ihara (1986)
Inventiones mathematicae
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Multiplicities of mod p Galois representations.
Chandrashekhar Khare (1998)
Manuscripta mathematica
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Explicit solutions to embedding problems associated to orthogonal Galois representations.
Teresa Crespo (1990)
Journal für die reine und angewandte Mathematik
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Galois coverings and the Clebsch-Gordan problem for quiver representations
Martin Herschend (2007)
Colloquium Mathematicae
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We study the Clebsch-Gordan problem for quiver representations, i.e. the problem of decomposing the point-wise tensor product of any two representations of a quiver into its indecomposable direct summands. For this purpose we develop results describing the behaviour of the point-wise tensor product under Galois coverings. These are applied to solve the Clebsch-Gordan problem for the double loop quivers with relations αβ = βα = αⁿ = βⁿ = 0. These quivers were originally studied by I....
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...