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Multiplicities and Chern Classes in Local Algebra

Part of Cambridge Tracts in Mathematics

  • Date Published: June 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521065832

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  • The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map.

    • First book to give a thorough account of use of Chern classes in commutative algebra
    • Does not require an extensive background in algebraic geometry
    • Includes recent research results
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    Reviews & endorsements

    Review of the hardback: '… a well-motivated survey of such a broad range of material, some of it quite technical, which leads the reader to the forefront of some of the deepest modern developments in Intersection Theory.' Proceedings of the Edinburgh Mathematical Society

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    Product details

    • Date Published: June 2008
    • format: Paperback
    • isbn: 9780521065832
    • length: 320 pages
    • dimensions: 230 x 150 x 20 mm
    • weight: 0.47kg
    • availability: Available
  • Table of Contents

    1. Prime ideals and the Chow group
    2. Graded rings and Samuel multiplicity
    3. Complexes and derived functors
    4. Homological properties of rings and modules
    5. Intersection multiplicities
    6. The homological conjectures
    7. The Frobenius map
    8. Projective schemes
    9. Chern classes of locally free sheaves
    10. The Grassmannian
    11. Local Chern characters
    12. Properties of local Chern characters
    13. Applications and examples.

  • Author

    Paul C. Roberts, University of Utah

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