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.
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