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Smoothness, Regularity and Complete Intersection

Part of London Mathematical Society Lecture Note Series

  • Date Published: June 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521125727

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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. 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.

    • Perfectly complements standard books in the field
    • Provides more elementary proofs, avoiding simplicial techniques
    • Useful resource for graduate students as well as researchers who are unfamiliar with simplicial methods
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    Reviews & endorsements

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

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    Product details

    • Date Published: June 2010
    • format: Paperback
    • isbn: 9780521125727
    • length: 140 pages
    • dimensions: 228 x 151 x 9 mm
    • weight: 0.22kg
    • availability: Available
  • 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
    Index.

  • Authors

    Javier Majadas, Universidad de Santiago de Compostela, Spain
    Javier Majadas is Professor at the University of Santiago de Compostela, Spain.

    Antonio G. Rodicio, Universidad de Santiago de Compostela, Spain
    Antonio G. Rodicio is Professor at the University of Santiago de Compostela, Spain.

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