Smoothness, Regularity and Complete Intersection

Smoothness, Regularity and Complete Intersection

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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 more

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' ... thisbook makes for a useful addition to the (rather meagre) literature on the uses of Andre-Quillen homology and cohomology in commutative algebra and algebraic geometry. Mathematical Reviewsshow more

About Javier Majadas

Javier Majadas is Professor at the University of Santiago de Compostela, Spain. Antonio G. Rodicio is Professor at the University of Santiago de Compostela, more

Table of contents

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; more