Explicit deformation of Galois representations.
Nigel Boston (1991)
Inventiones mathematicae
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Nigel Boston (1991)
Inventiones mathematicae
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B. Mazur (1990)
Compositio Mathematica
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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.
Ami Fischman (2002)
Annales de l’institut Fourier
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We explore the question of how big the image of a Galois representation attached to a -adic modular form with no complex multiplication is and show that for a “generic” set of -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.
Robert C. Valentini (1986)
Mathematische Zeitschrift
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Shankar Sen (1980/81)
Inventiones mathematicae
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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...
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.
Wintenberger, J.-P. (2007)
Documenta Mathematica
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Skinner, Christopher (2009)
Documenta Mathematica
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H. Hida (1986)
Inventiones mathematicae
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