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
