ALGEBRAIC GEOMETRY

By: BUMP D

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Hardcover | 9 December 1998

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230 Pages

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22.86 x 15.24 x 1.42

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This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is 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 a selection of topics from the theory of algebraic curves, including the Riemann–Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.

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Non-Fiction Mathematics Geometry Algebraic Geometry Number Theory Analytic Geometry Booktopia Publisher Services World Scientific Publishing

Preface
Information for the Reader
Affine Algebraic Sets and Varieties	p. 1
The Extension Theorem	p. 7
Maps of Affine Varieties	p. 13
Dimension and Products	p. 23
Local Algebra	p. 39
Properties of Affine Varieties	p. 61
Varieties	p. 79
Complete Nonsingular Curves	p. 97
Ramification	p. 103
Completions	p. 125
Differentials and Residues	p. 137
The Riemann-Roch Theorem	p. 159
Elliptic Curves and Abelian Varieties	p. 175
The Zeta Function of a Curve	p. 195
References	p. 211
Index	p. 215
Table of Contents provided by Blackwell. All Rights Reserved.

ALGEBRAIC GEOMETRY

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Hardcover

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