Smoothness Regularity And Complete Intersection

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Smoothness, Regularity and Complete Intersection

Author: Javier Majadas
language: en
Publisher: Cambridge University Press
Release Date: 2010-05-06
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.
Smoothness, Regularity and Complete Intersection

Author: Javier Majadas
language: en
Publisher: Cambridge University Press
Release Date: 2010-05-06
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.
O-Minimality and Diophantine Geometry

Author: G. O. Jones
language: en
Publisher: Cambridge University Press
Release Date: 2015-08-13
This book brings the researcher up to date with recent applications of mathematical logic to number theory.