Algebraic Geometry

Front Cover
World Scientific, 1998 - Mathematics - 218 pages
2 Reviews
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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Contents

Affine Algebraic Sets and Varieties
1
The Extension Theorem
7
Maps of Affine Varieties
13
Dimension and Products
23
Local Algebra
39
Properties of Affine Varieties
61
Varieties
79
Complete Nonsingular Curves
97
Completions
125
Differentials and Residues
137
The RiemannRoch Theorem
159
Elliptic Curves and Abelian Varieties
175
The Zeta Function of a Curve
195
References
211
Index
215
Copyright

Ramification
103

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