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Smoothness, Regularity and Complete Intersection

Javier Majadas Antonio G. Rodicio

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Cambridge University Press
06 May 2010
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. Andre) and localisation of complete intersections (L. Avramov), some important results of D. Popescu and Andre on regular homomorphisms, and some results from A. Grothendieck's EGA on smooth homomorphisms. The authors make extensive use of the Andre-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.
By:   Javier Majadas, Antonio G. Rodicio
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Dimensions:   Height: 228mm,  Width: 151mm,  Spine: 9mm
Weight:   220g
ISBN:   9780521125727
ISBN 10:   0521125723
Series:   London Mathematical Society Lecture Note Series
Publication Date:   06 May 2010
Audience:   Professional and scholarly ,  Undergraduate ,  Further / Higher Education
Format:   Paperback
Publisher's Status:   Active
Introduction; 1. Definition and first properties of (co-)homology modules; 2. Formally smooth homomorphisms; 3. Structure of complete noetherian local rings; 4. Complete intersections; 5. Regular homomorphisms: Popescu's theorem; 6. Localization of formal smoothness; Appendix: some exact sequences; Bibliography; Index.

Reviews for Smoothness, Regularity and Complete Intersection

This book makes for a useful addition to the (rather meager) literature on the uses of Andre-Quillen homology and cohomology in commutative algebra and algebraic geometry. Srikanth B. Iyengar, Mathematical Reviews

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