Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / Nancy Childress, John W. Jones, editors.

Format:

Book

Conference/Event

Author/Creator:

Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, Corporate Author.

Contributor:

Childress, Nancy, 1958- editor.

Jones, John W., 1961- editor.

Conference Name:

Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory (1993 : Arizona state University)

Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 174

Contemporary mathematics, 0271-4132 ; 174

Language:

English

Subjects (All):

Algebraic number theory--Congresses.

Algebraic number theory.

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Iwasawa theory--Congresses.

Iwasawa theory.

Physical Description:

1 online resource (ix, 220 p. )

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1994]

Language Note:

English

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 computation of torsion groups of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations. With contributions by some of the leading experts in the field, this book provides a look at the state of the art in arithmetic geometry.

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 Lω.

2.1. - Valeur de Lω en X-jn pour j &gt

1

2.2. - Valeur de Lω en X-jn pour j &lt

0

2.3. - Valeur de Lω en X-1n et en n

3. - Fonction de Kubota-Leopoldt.

3.1. - Définition.

3.2. - Valeurs de LK-L en X-jn

3.3. - "Conjecture" principale.

4. - Cohomologie galoisienne.

4.1. - Notations.

4.2. - Cohomologie galoisienne et dimensions

4.3. - 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

Λ-adic modular forms of half-integral weight and a Λ-adic Shintani lifting

The 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

1.1. Acknowledgments

2. Preliminaries

2.1. Classical Modular Forms

2.2. Formulaire Elliptique

2.3. The Taylor coefficients of θ

3. Taylor Coefficients of θ 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 Measures.

4.2. P-adic Factorization Formulas

4.3. P-adic Interpolation

4.4. P-adic θ

Torsion groups of elliptic curves over cubic and certain biquadratic number fields.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-7765-8

0-8218-5511-5