Contents

Preface

Real Hilbertianity and the field of totally real numbers

MICHAEL D. FRIED, DAN HARAN, AND HELMUT VOLKLEIN

1

Galois groups with prescribed ramification

DAVID HARBATER

35

Note on the zeros of p-adic £-functions

TAUNO METSANKYLA

61

La fonction

L

p-adique de Kubota-Leopoldt

BERNADETTE PERRIN-RIOU

65

Supersingular p-adic height pairings on elliptic curves

ANDREW PLATER

95

Fields of definition of abelian varieties with real multiplication

KENNETH A. RIBET

107

p-adic interpolation of half-integral weight modular forms

ADRIANA SOFER

119

A-adic

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

GLENN STEVENS

129

The non-existence of certain Galois extensions of

Q

unramified outside 2

JOHN TATE

153

Iwasawa theory and cyclotomic function fields

DINESH S. THAKUR

157

Slopes of modular forms

DOUGLAS

L.

ULMER

167

On the Taylor coefficients of theta functions of CM elliptic curves

FERNANDO RODRIGUEZ VILLEGAS

185

Torsion groups of elliptic curves over cubic and certain biquadratic number

fields

HORST G. ZIMMER

vii

203