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Galois representations
 Proceedings of the International Congress of Mathematicians, Beijing, 2002, vol I. World Scientific
"... In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie groups. In the second part we briefly review some limited re ..."
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In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie groups. In the second part we briefly review some limited
Galois representations
, 2015
"... Let y2 = x3 +Ax +B be an elliptic curve over a number field K. Let K (E [m]) be the extension of K obtained by adjoining the coordinates of all the mtorsion points of E(K). This is a Galois extension, and Gal(K (E [m])/K) acts on E [m] ' Z/m ⊕ Z/m ..."
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Let y2 = x3 +Ax +B be an elliptic curve over a number field K. Let K (E [m]) be the extension of K obtained by adjoining the coordinates of all the mtorsion points of E(K). This is a Galois extension, and Gal(K (E [m])/K) acts on E [m] ' Z/m ⊕ Z/m
DEFORMATION THEORY OF GALOIS REPRESENTATIONS
"... Local torsion on elliptic curves and the deformation theory of galois representations ..."
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Local torsion on elliptic curves and the deformation theory of galois representations
Galois representations attached to representations
"... Abstract. For a fixed prime ∈ Z we compute the adic Lie algebra of the image of the adic Galois representation ρ attached to a stable cuspidal automorphic representation π of the unitary similitude groupGU(3). This result depends on whether π admits extra twists in the sense defined below. Two c ..."
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Abstract. For a fixed prime ∈ Z we compute the adic Lie algebra of the image of the adic Galois representation ρ attached to a stable cuspidal automorphic representation π of the unitary similitude groupGU(3). This result depends on whether π admits extra twists in the sense defined below. Two
On threedimensional Galois representations
, 2006
"... We give an irreducibility criterion for the Galois images of compatible ladic systems of Galois representations. We apply this to the ladic realizations of the van GeemenTop motive M and prove an analogue of Serre’s theorem for M. 1 ..."
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We give an irreducibility criterion for the Galois images of compatible ladic systems of Galois representations. We apply this to the ladic realizations of the van GeemenTop motive M and prove an analogue of Serre’s theorem for M. 1
Galois representations and modular forms
, 2006
"... This note is based on a series of lectures given at the summer school held on July 1729, 2006 at IHES. The purpose of the lectures is to explain the basic ideas in the geometric construction of the Galois representations associated to elliptic modular forms of weight at least 2. ..."
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This note is based on a series of lectures given at the summer school held on July 1729, 2006 at IHES. The purpose of the lectures is to explain the basic ideas in the geometric construction of the Galois representations associated to elliptic modular forms of weight at least 2.
Étale cohomology and Galois Representations
, 2012
"... In this essay we briefly introduce the main ideas behind the theory of studying algebraic varieties over a number field by constructing associated Galois representations, and see how this can be understood naturally in the context of an extension of monodromy theory from geometry. We then, following ..."
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In this essay we briefly introduce the main ideas behind the theory of studying algebraic varieties over a number field by constructing associated Galois representations, and see how this can be understood naturally in the context of an extension of monodromy theory from geometry. We then
MODULAR FORMS AND THEIR GALOIS REPRESENTATIONS
"... In this course, assuming basic knowledge of algebraic number theory, commutative algebra and topology, we study nonarchimedean deformation theory of modular forms on GL(2) and modular Galois representations into GL(2). We plan to discuss the following four topics: (1) analytic/algebraic theory of e ..."
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In this course, assuming basic knowledge of algebraic number theory, commutative algebra and topology, we study nonarchimedean deformation theory of modular forms on GL(2) and modular Galois representations into GL(2). We plan to discuss the following four topics: (1) analytic/algebraic theory
Results 1  10
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20,777