Contemporary Mathematics 1994; 220 pp; softcover Volume: 174 ISBN10: 0821851748 ISBN13: 9780821851746 List Price: US$59 Member Price: US$47.20 Order Code: CONM/174
 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 halfintegral 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 The volume also contains a previously unpublished letter of John Tate, written to J.P. Serre in 1973, concerning Serre's conjecture on Galois representations.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  M. D. Fried, D. Haran, and H. Völklein  Real Hilbertianity and the field of totally real numbers
 D. Harbater  Galois groups with prescribed ramification
 T. Metsänkylä  Note on the zeros of \(p\)adic \(L\)functions
 B. PerrinRiou  La fonction \(L p\)adique de KubotaLeopoldt
 A. Plater  Supersingular \(p\)adic height pairings on elliptic curves
 K. A. Ribet  Fields of definition of Abelian varieties with real multiplication
 A. Sofer  \(p\)adic interpolation of halfintegral weight modular forms
 G. Stevens  \(\Lambda\)adic modular forms of halfintegral weight and a \(\Lambda\)adic Shintani lifting
 J. Tate  The nonexistence of certain Galois extensions of \(\mathbb Q\) unramified outside \(2\)
 D. S. Thakur  Iwasawa theory and cyclotomic function fields
 D. L. Ulmer  Slopes of modular forms
 F. R. Villegas  On the Taylor coefficients of theta functions of \(CM\) elliptic curves
 H. G. Zimmer  Torsion groups of elliptic curves over cubic and certain biquadratic number fields
