| Description |
1 online resource (203 pages) |
| Series |
Research Notes in Mathematics Ser. ; v. 7 |
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Research Notes in Mathematics Ser
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Special Preface; Preface; Vita; Table of Contents; INTRODUCTION; NOTATIONS; Chapter I: l-adic Representations; Â1 The notion of an l-adic representation; 1.1 Definition; 1.2 Examples; Â2 l-adic representations of number fields; 2.1 Preliminaries; 2.2 Cebotarev's density theorem; 2.3 Rationall-adic representations; 2.4 Representations with values in a linear algebraic group; 2.5 L-functions attached to rational representations; Appendix Equipartition and L-functions; A.1 Equipartition; A.2 The connection with L-functions; A.3 Proof of theorem 1 |
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Chapter II: The Groups SmÂ1 Preliminaries; 1.1 The torus T; 1.2 Cutting down T; 1.3 Enlarging groups; Â2 Construction of Tm and Sm; 2.1 IdÃl̈es and idÃl̈e-classes; 2.2 The groups Tm and Sm; 2.3 The canonical l-adic representation with values in Sm; 2.4 Linear representations of Sm; 2.5 l-adic representations associated to a linear representation of Sm; 2.6 Alternative construction; 2.7 The real case; 2.8 An example: complex multiplication of abelian varieties; Â3 Structure of Tm and applications; 3.1 Structure of X(Tm); 3.2 The morphism j* : Gm â#x86;#x92; Tm; 3.3 Structure of Tm |
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3.4 How to compute FrobeniusesAppendix Killing arithmetic groups in tori; A.1 Arithmetic groups in tori; A.2 Killing arithmetic subgroups; Chapter Ill: Locally Algebraic Abelian Representations; Â1 The local case; 1.1 Definitions; 1.2 Alternative definition of ""locally algebraic"" via Hodge-Tate modules; Â2 The global case; 2.1 Definitions; 2.2 Modulus of a locally algebraic abelian representation; 2.3 Back to Sm; 2.4 A mild generalization; 2.5 The function field case; Â3 The case of a composite of quadratic fields; 3.1 Statement of the result; 3.2 A criterion for local algebraicity |
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3.3 An auxiliary result on tori3.4 Proof of the theorem; Appendix Hodge-Tate decompositions and locally algebraic representations; A.1 lnvariance of Hodge-Tate decompositions; A.2 Admissible characters; A.3 A criterion for local triviality; A.4 The character ÎℓE; A.5 Characters associated with Hodge-Tate decompositions; A.6 Locally compact case; A.7 Tate's theorem; Chapter IV: l-adic Representations Attached to Elliptic Curves; Â1 Preliminaries; 1.1 Elliptic curves; 1.2 Good reduction; 1.3 Properties of V1 related to good reduction; 1.4 SafareviÄ#x8D;' s theorem |
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Â2 The Galois modules attached to E2.1 The irreducibility theorem; 2.2 Determination of the Lie algebra of G1; 2.3 The isogeny theorem; Â3 Variation of Gl and GÌ#x83;l with l; 3.1 Preliminaries; 3.2 The case of a non integral j; 3.3 Numerical example; 3.4 Proof of the main lemma of 3.1; Appendix Local results; A.1 The case v(j) <0; A.1.1. The elliptic curves of Tate; A.1.2 An exact sequence; A.1.4 Application to isogenies; A.1.5 Existence of transvections in the inertia group; A.2 The case v(j) â#x89;Æ 0; A.2.1 The case 1 â#x89; p; A.2.2 The case 1 = p with good reduction of height 2 |
| Notes |
A.2.3 Auxiliary results on abelian varieties |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Representations of groups.
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Curves, Elliptic.
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Algebraic fields.
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MATHEMATICS -- Algebra -- Intermediate.
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Algebraic fields
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Curves, Elliptic
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Representations of groups
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Elliptische Kurve
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Kommutative Algebra
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| Form |
Electronic book
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| ISBN |
9781439863862 |
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1439863865 |
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