UID:
almafu_9959227384602883
Format:
1 online resource (vi, 134 pages) :
,
digital, PDF file(s).
ISBN:
1-107-20357-0
,
1-139-10718-6
,
1-283-29602-0
,
1-139-12290-8
,
9786613296023
,
1-139-12782-9
,
1-139-11716-5
,
1-139-11280-5
,
1-139-11499-9
Series Statement:
London Mathematical Society lecture note series ; 373
Content:
Written to complement standard texts on commutative algebra, this short book gives complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. André) and localisation of complete intersections (L. Avramov), some important results of D. Popescu and André on regular homomorphisms, and some results from A. Grothendieck's EGA on smooth homomorphisms. The authors make extensive use of the André-Quillen homology of commutative algebras, but only up to dimension 2, which is easy to construct, and they deliberately avoid using simplicial methods. The book also serves as an accessible introduction to some advanced topics and techniques. The only prerequisites are a basic course in commutative algebra and the first definitions in homological algebra.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
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
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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
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6.4 End of the proof of localization of formal smoothness6.5 Appendix: Power series; Appendix: Some exact sequences; Bibliography; Index
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English
Additional Edition:
ISBN 0-521-12572-3
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9781139107181
