Title Arithmetic Geometry

Published Providence : American Mathematical Society, 1994

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Description 1 online resource (234 pages) Series Contemporary Mathematics Ser. ; v. 174 Contemporary Mathematics Ser Contents Intro; Contents; Preface; Real Hilbertianity and the field of totally real numbers; Galois groups with prescribed ramification; Note on the zeros of p-adic L-functions; La fonction L p-adique de Kubota-Leopoldt; 1. -- Rappels.; 2. -- Quelques formules sur LÏ#x89;.; 2.1. -- Valeur de LÏ#x89; en Xâ#x80;#x93;jn pour j> 1; 2.2. -- Valeur de LÏ#x89; en Xâ#x80;#x93;jn pour j <0; 2.3. -- Valeur de LÏ#x89; en Xâ#x80;#x93;1n et en n; 3. -- Fonction de Kubota-Leopoldt.; 3.1. -- Définition.; 3.2. -- Valeurs de LKâ#x80;#x93;L en Xâ#x80;#x93;jn; 3.3. -- ""Conjecture"" principale.; 4. -- Cohomologie galoisienne.; 4.1. -- Notations 4.2. -- Cohomologie galoisienne et dimensions4.3. -- Démonstrations par la méthode de Kolyvagin; 5. -- Conjectures sur les valeurs spéciales.; Supersingular p-adic height pairings on elliptic curves; Fields of definition of abelian varieties with real multiplication; p-adic interpolation of half-integral weight modular forms; 1. Introduction; 2. Definitions and properties; 2.1. p-adic modular forms; 2.2. The q-expansion principle; 2.3. Measures; 3. Interpolation; 3.1. The measure associated to a modular form; 3.2. Restriction of the measure to pZp; 4. Applications; References Î#x9B;-adic modular forms of half-integral weight and a Î#x9B;-adic Shintani liftingThe non-existence of certain Galois extensions of Q unramified outside 2; Iwasawa theory and cyclotomic function fields; Slopes of modular forms; On the Taylor coefficients of theta functions of CM elliptic curves; 1. Introduction; 1.1. Acknowledgments; 2. Preliminaries; 2.1. Classical Modular Forms; 2.2. Formulaire Elliptique; 2.3. The Taylor coefficients of Îı; 3. Taylor Coefficients of Îı and Square Roots of Central Values; 3.1. The Elliptic Curves A(l); 3.2. The Formula; 4. Interpolation 4.1. P-adic Modular Forms and Theta Measures4.2. P-adic Factorization Formulas; 4.3. P-adic Interpolation; 4.4. P-adic Îı; References; Torsion groups of elliptic curves over cubic and certain biquadratic number fields Summary This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral weight and their roles in arithmetic geometry. The volume also contains material on the Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including p-adic L-functions and p-adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and comp Notes Print version record Subject Algebraic number theory -- Congresses Geometry, Algebraic -- Congresses Iwasawa theory -- Congresses Algebraic number theory Geometry, Algebraic Iwasawa theory Genre/Form Conference papers and proceedings Form Electronic book Author Jones, John W ISBN 9780821877654 0821877658

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