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9780821851746

Arithmetic Geometry

by ; ;
  • ISBN13:

    9780821851746

  • ISBN10:

    0821851748

  • Format: Paperback
  • Copyright: 1994-12-01
  • Publisher: Amer Mathematical Society

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Supplemental Materials

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 The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations.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

Table of Contents

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
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
$\Lambda$-adic modular forms of half-integral weight and a $\Lambda$-adic Shintani lifting
The non-existence of certain Galois extensions of $\mathbb Q$ unramified outside $2$
Iwasawa theory and cyclotomic function fields
Slopes of modular forms
On the Taylor coefficients of theta functions of $CM$ elliptic curves
Torsion groups of elliptic curves over cubic and certain biquadratic number fields
Table of Contents provided by Publisher. All Rights Reserved.

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