Displaying similar documents to “Galois representations”

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.

Functoriality and the Inverse Galois problem II: groups of type B n and G 2

Chandrashekhar Khare, Michael Larsen, Gordan Savin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and t a positive integer. We show that that the finite simple groups of Lie type B n ( k ) = 3 D S O 2 n + 1 ( 𝔽 k ) d e r if 3 , 5 ( mod 8 ) and G 2 ( k ) appear as Galois groups over , for some k divisible by t . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise...

Automorphy for some l-adic lifts of automorphic mod l Galois representations

Laurent Clozel, Michael Harris, Richard Taylor (2008)

Publications Mathématiques de l'IHÉS

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We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we...