**Contemporary Mathematics**

Volume: 174;
1994;
220 pp;
Softcover

MSC: Primary 11;
Secondary 12

Print ISBN: 978-0-8218-5174-6

Product Code: CONM/174

List Price: $62.00

AMS Member Price: $49.60

MAA Member Price: $55.80

**Electronic ISBN: 978-0-8218-7765-4
Product Code: CONM/174.E**

List Price: $62.00

AMS Member Price: $49.60

MAA Member Price: $55.80

# Arithmetic Geometry

Share this page *Edited by *
*Nancy Childress; John W. Jones*

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 The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations.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.

#### Readership

Researchers and advanced graduate students working in number theory and arithmetic geometry.

# Table of Contents

## Arithmetic Geometry

- Contents vii8 free
- Preface ix10 free
- Real Hilbertianity and the field of totally real numbers 112 free
- Galois groups with prescribed ramification 3546
- Note on the zeros of p-adic L-functions 6172
- La fonction L p-adique de Kubota-Leopoldt 6576
- Supersingular p-adic height pairings on elliptic curves 95106
- Fields of definition of abelian varieties with real multiplication 107118
- p-adic interpolation of half-integral weight modular forms 119130
- Λ-adic modular forms of half-integral weight and a Λ-adic Shintani lifting 129140
- The non-existence of certain Galois extensions of Q unramified outside 2 153164
- Iwasawa theory and cyclotomic function fields 157168
- Slopes of modular forms 167178
- On the Taylor coefficients of theta functions of CM elliptic curves 185196
- Torsion groups of elliptic curves over cubic and certain biquadratic number fields 203214