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  3. Smoothness, Regularity and Complete Intersection
  • Cited by 11
Publisher:
Cambridge University Press
Online publication date:
September 2011
Print publication year:
2010
Online ISBN:
9781139107181
DOI:
https://doi.org/10.1017/CBO9781139107181
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
London Mathematical Society Lecture Note Series (373)
Information

Book description

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.

Reviews

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

Source: Mathematical Reviews

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