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326
Foliations in Moduli Spaces of Abelian Varieties
 Journ. Amer. Math. Soc
, 2002
"... In this paper we study abelian varieties and of pdivisible groups in characteristic p. Even though a nontrivial deformation... ..."
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Cited by 85 (21 self)
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In this paper we study abelian varieties and of pdivisible groups in characteristic p. Even though a nontrivial deformation...
Cuspidality of symmetric powers with applications
 Duke Math. J
"... The purpose of this paper is to prove that the symmetric fourth power of a cusp form on GL(2), whose existence was proved earlier by the first author, is cuspidal unless the corresponding automorphic representation is of dihedral, tetrahedral, or octahedral type. As a consequence, we prove a number ..."
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Cited by 61 (4 self)
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The purpose of this paper is to prove that the symmetric fourth power of a cusp form on GL(2), whose existence was proved earlier by the first author, is cuspidal unless the corresponding automorphic representation is of dihedral, tetrahedral, or octahedral type. As a consequence, we prove a number of results toward the Ramanujanfor unramified Hecke eigenvalues of cusp forms on GL(2). Over an arbitrary number field, this is the best bound available at present. Petersson and SatoTate conjectures. In particular, we establish the bound q 1/9 v 1.
Functorial products for GL2 × GL3 and the symmetric cube for GL2
 ANN. OF MATH
, 2002
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SYMPLECTIC LOCAL ROOT NUMBERS, CENTRAL CRITICAL LVALUES, AND RESTRICTION PROBLEMS IN THE REPRESENTATION THEORY OF CLASSICAL GROUPS
"... We give a conjectural description of the restriction of an irreducible representation of a unitary group U(n) to a subgroup U(n − 1) over a local or global field. We formulate analogous conjectures for the restriction problem from U(n) to a subgroup U(m) (m < n) using Bessel and FourierJacobi m ..."
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Cited by 51 (6 self)
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We give a conjectural description of the restriction of an irreducible representation of a unitary group U(n) to a subgroup U(n − 1) over a local or global field. We formulate analogous conjectures for the restriction problem from U(n) to a subgroup U(m) (m < n) using Bessel and FourierJacobi models, and also similar restriction problems for symplectic groups. The conjectures are analogs of those in [GP1] and [GP2] for the orthogonal groups. We verify these conjectures in certain low rank cases and for depth zero supercuspidal representations, and prove that the conjectures about Bessel and FourierJacobi models follow from the conjectural description of the restriction of an irreducible representation of a unitary group U(n) (resp. SO(n)) to a subgroup U(n −1)
Compatibility of local and global Langlands correspondences
 J. Amer. Math. Soc
, 2007
"... Abstract. We prove the compatibility of local and global Langlands correspondences for GLn, which was proved up to semisimplification in [HT]. More precisely, for the ndimensional ladic representation Rl(Π) of the Galois group of a CMfield L attached to a conjugate selfdual regular algebraic cusp ..."
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Cited by 47 (12 self)
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Abstract. We prove the compatibility of local and global Langlands correspondences for GLn, which was proved up to semisimplification in [HT]. More precisely, for the ndimensional ladic representation Rl(Π) of the Galois group of a CMfield L attached to a conjugate selfdual regular algebraic cuspidal automorphic representation Π, which is square integrable at some finite place, we show that Frobenius semisimplification of the restriction of Rl(Π) to the decomposition group of a prime v of L not dividing l corresponds to Πv by the local Langlands correspondence.