Ideals and Reality

Projective Modules and Numbers of Generators of Ideals

Friedrich Ischebeck, Ravi Rao - Collection Springer Monographs in Mathematics

336 pages, parution le 13/12/2004

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Résumé

This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in n-space is a set-theoric intersection, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratýnski.

The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises.

Even this advanced material, presented comprehensively, keeps in mind the young student as potential reader besides the specialists of the subject.

Sommaire

Basic Commutative Algebra 1
Introduction to Projective Modules
Stably Free Modules
Serre's Conjecture
Basic Commutative Algebra II
Splitting Theorem and Lindel's Proof
Regular Rings
Number of Generators
Curves as Complete Intersection
Normality of E_n, in GL_n
Some Homological Algebra
Complete intersections and Connectedness
Odds and Ends
Exercices
References
Index

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Friedrich Ischebeck, Ravi Rao
Collection	Springer Monographs in Mathematics
Parution	13/12/2004
Nb. de pages	336
Format	16 x 24
Couverture	Relié
Poids	640g
Intérieur	Noir et Blanc
EAN13	9783540230328