Cover; Title; Copyright; Contents; Introduction; 1 Definition and first properties of (co- )homology modules; 1.1 First definition; 1.2 Differential graded algebras; 1.3 Second definition; 1.4 Main properties; 2 Formally smooth homomorphisms; 2.1 Infinitesimal extensions; 2.2 Formally smooth algebras; 2.3 Jacobian criteria; 2.4 Field extensions; 2.5 Geometric regularity; 2.6 Formally smooth local homomorphisms of noetherian rings; 2.7 Appendix: The Mac Lane separability criterion; 3 Structure of complete noetherian local rings; 3.1 Cohen rings; 3.2 Cohen's structure theorems
4 Complete intersections4.1 Minimal DG resolutions; 4.2 The main lemma; 4.3 Complete intersections; 4.4 Appendix: Kunz's theorem on regular local rings in characteristic p; 5 Regular homomorphisms: Popescu's theorem; 5.1 The Jacobian ideal; 5.2 The main lemmas; 5.3 Statement of the theorem; 5.4 The separable case; 5.5 Positive characteristic; 5.6 The module of differentials of a regular homomorphism; 6 Localization of formal smoothness; 6.1 Preliminary reductions; 6.2 Some results on vanishing of homology; 6.3 Noetherian property of the relative Frobenius
6.4 End of the proof of localization of formal smoothness6.5 Appendix: Power series; Appendix: Some exact sequences; Bibliography; Index
Summary
This short book gives complete and relatively easy proofs of well-known important results found in standard books on commutative algebra. It also serves as a friendly introduction to the powerful methods used in the Andre-Quillen homology of commutative algebras
Bibliography
Includes bibliographical references (pages 130-133) and index
