Galois representations, embedding problems and modular forms.

Teresa Crespo

Displaying similar documents to “Galois representations, embedding problems and modular forms.”

The absolute Galois group of a pseudo real closed field

Dan Haran, Moshe Jarden (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Modularity of an odd icosahedral representation

Arnaud Jehanne, Michael Müller (2000)

Journal de théorie des nombres de Bordeaux

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In this paper, we prove that the representation $ρ$ from $G_{ℚ}$ in GL $_{2} (ℂ)$ with image $A_{5}$ in PGL $_{2} (A_{5})$ corresponding to the example $16$ in [B-K] is modular. This representation has conductor $5203$ and determinant $χ_{- 43}$ ; its modularity was not yet proved, since this representation does not satisfy the hypothesis of the theorems of [B-D-SB-T] and [Tay2].

Differential Galois realization of double covers

Teresa Crespo, Zbigniew Hajto (2002)

Annales de l’institut Fourier

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An effective construction of homogeneous linear differential equations of order 2 with Galois group $2 A_{4}, 2 S_{4}$ or $2 A_{5}$ is presented.

Precise study of some number fields and Galois actions occurring in conformal field theory

E. Buffenoir, A. Coste, J. Lascoux, P. Degiovanni, A. Buhot (1995)

Annales de l'I.H.P. Physique théorique

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P-division points on certain elliptic curves

Kuang-Yen Shih (1978)

Compositio Mathematica

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Polynomials of Galois representations attached to elliptic curves.

A. Reverter, N. Vila (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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On realizability of p-groups as Galois groups

Michailov, Ivo M., Ziapkov, Nikola P. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12, 15A66. In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related...

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, $p$ -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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Quaternion Extensions of Order 16

Michailov, Ivo (2005)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12 We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16. This work is partially supported by project of Shumen University.