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ALGEBRAIC GEOMETRY
by Daniel Bump (Stanford University)
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.
Contents:
- Affine Algebraic Sets and Varieties
- The Extension Theorem
- Maps of
Affine Varieties
- Dimensions and Products
- Local Algebra
- Properties of Affine Varieties
- Varieties
- Complete Nonsingular Curves
- Ramification
- Completions
- Differentials and Residues
- The Riemann–Roch Theorem
- Elliptic Curves and Abelian Varieties
- The Zeta Function of a Curve
Readership: Graduate students in mathematics.
"Summing up, this book provides an introduction to algebraic geometry which is certainly more algebraic (or arithmetic) than geometric ... The exposition is extremely clear, comprehensive and rigorous, and the many (challenging) exercises following each chapter are very deliberately selected. This book is a very valuable enhancement to the current textbook literature on (geometric) algebraic geometry, and a recommendable introduction to arithmetic geometry just as well."
| 228pp |
Pub. date: Dec 1998 |
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