Algebraic geometry

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. Booknews A text for a one-year course at the graduate level, for students with substantial background in algebra. Eight chapters contain material applicable to varieties of every dimension, and six chapters contain material which is particular to the theory of curves. Material considers irreducible varieties over an algebraically closed field, except in one chapter, which works over a finite field. Coverage includes the extension theorem, maps of affine varieties, complete nonsingular curves, and the Riemann-Roch theory. Intersection theory is not covered. Includes chapter exercises. The author teaches mathematics at Stanford University. Annotation c. Book News, Inc., Portland, OR (booknews.com) "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."- This text presents algebraic geometry, providing self-contained development of the fundamentals, including all commutative algebras which are used. It culminates with the theory of curves, including the Riemann-Roch theorem, elliptic curves and the zeta function of a curve over a finite field.