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  3. Smoothness, Regularity and Complete Intersection
  • Cited by 12
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2011
      May 2010
      ISBN:
      9781139107181
      9780521125727
      DOI:
      https://doi.org/10.1017/CBO9781139107181
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.22kg, 140 Pages
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      London Mathematical Society Lecture Note Series (373)
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    • Selected: Digital
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    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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