An Algebraic Introduction to Complex Projective Geometry Commutative Algebra 1st Edition by Christian Peskine ISBN 0521480728 9780521480727

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Product details:

ISBN 10: 0521480728

ISBN 13: 9780521480727 

Author: Christian Peskine 

In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether’s normalization lemma and Hilbert’s Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski’s main theorem and Chevalley’s semi-continuity theorem. Finally, the author’s detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.

Table of contents:

1. Rings, homomorphisms, ideals

2. Modules

3. Noetherian rings and modules

4. Artinian rings and modules

5. Finitely generated modules over Noetherian rings

6. A first contact with homological algebra

7. Fractions

8. Integral extensions of rings

9. Algebraic extensions of rings

10. Noether’s normalisation lemma

11. Affine schemes

12. Morphisms of affine schemes

13. Zariski’s main theorem

14. Integrally closed Noetherian rings

15. Weil divisors

16. Cartier divisors

17. Subject index

18. Symbols index

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Tags: Christian Peskine, Algebraic Introduction, Complex Projective Geometry, Commutative Algebra