Simple Morphisms in Algebraic Geometry

Richard Sot (auth.)0387115641, 9780387115641

Table of contents :
The Zariski topology, the Jacobian criterion and examples of simple algebras over a field k….Pages 1-17
The Kahler 1-differentials….Pages 18-34
Every k-algebra a which is essentially of finite type over k and simple is a regular local ring….Pages 35-44
Brief discussion of unramified and étale homomorphisms….Pages 45-53
Some corollaries to Theorem 3.5….Pages 54-56
Fitting ideals….Pages 57-72
Proof of the Jacobian criterion and some characterizations of simple k-algebras and A-algebras….Pages 73-88
Characterizations of simple A-algebras in terms of étale homomorphisms; invariance of the property of being a simple algebra under composition and change of base….Pages 89-102
Descent of simple homomorphisms and removal of all noetherian assumptions in Chapter 7 and Chapter 8….Pages 103-116
Simple morphisms of preschemes and translation of previous theorems into the language of preschemes….Pages 117-127