Projective Modules and Complete Intersections

Satya Mandal (auth.)3540635645, 9783540635642

In these notes on “Projective Modules and Complete Intersections” an account on the recent developments in research on this subject is presented. The author’s preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead’s idea of the “generalized dimension functions”. These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.

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Table of contents :
Introduction….Pages 1-2
Preliminaires….Pages 3-12
Patching modules and other preliminaries….Pages 13-23
Extended modules over polynomial rings….Pages 25-33
Modules over commutative rings….Pages 35-62
The theory of matrices….Pages 63-72
Complete intersections….Pages 73-90
The techniques of lindel….Pages 91-110