代数几何ALGEBRAIC GEOMETRY

作者简介

This is a graduate 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.

书籍目录

PrefaceInformation for the Reader1. Affine Algebraic Sets and Varieties2. The Extension Theorem3. Maps of Affine Varieties4. Dimension and Products5. Local Algebra6. Properties of Affine Varieties7. Varieties8. Complete Nonsingular Curves9. Ramification10. Completions11. Differentials and Residues12. The Riemann-Roch Theorem13. Elliptic Curves and Abelian Varieties14. The Zeta Function of a CurveReferencesIndex

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