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9789810235611

ALGEBRAIC GEOMETRY

by
  • ISBN13:

    9789810235611

  • ISBN10:

    9810235615

  • Format: Nonspecific Binding
  • Copyright: 1998-12-07
  • Publisher: World Scientific Publishing
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Summary

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebras which are used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with the theory of curves, including the Riemann-Roch theorem, elliptic curves and the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.

Table of Contents

Preface v
Information for the Reader ix
Affine Algebraic Sets and Varieties
1(6)
The Extension Theorem
7(6)
Maps of Affine Varieties
13(10)
Dimension and Products
23(16)
Local Algebra
39(22)
Properties of Affine Varieties
61(18)
Varieties
79(18)
Complete Nonsingular Curves
97(6)
Ramification
103(22)
Completions
125(12)
Differentials and Residues
137(22)
The Riemann-Roch Theorem
159(16)
Elliptic Curves and Abelian Varieties
175(20)
The Zeta Function of a Curve
195(16)
References 211(4)
Index 215

Supplemental Materials

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