Simple Morphisms in Algebraic Geometry

Description

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