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Arithmetic Geometry
Edited by: Nancy Childress and John W. Jones
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Contemporary Mathematics
1994; 220 pp; softcover
Volume: 174
ISBN-10: 0-8218-5174-8
ISBN-13: 978-0-8218-5174-6
List Price: US$59
Member Price: US$47.20
Order Code: CONM/174
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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 The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations.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

  • 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. Perrin-Riou -- La fonction \(L p\)-adique de Kubota-Leopoldt
  • 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 half-integral weight modular forms
  • G. Stevens -- \(\Lambda\)-adic modular forms of half-integral weight and a \(\Lambda\)-adic Shintani lifting
  • J. Tate -- The non-existence 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
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