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Transcendental Aspects of Algebraic Cycles

Transcendental Aspects of Algebraic Cycles
Proceedings of the Grenoble Summer School, 2001


Part of London Mathematical Society Lecture Note Series

J. Elizondo, C. Peters, S. Kosarew, P. Lima-Filho, J. P. Murre, P. Elbaz-Vincent, J. D. Lewis, J. Nagel, S. Saito
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  • Date Published: April 2004
  • availability: In stock
  • format: Paperback
  • isbn: 9780521545471

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About the Authors
  • This is a collection of lecture notes from the Summer School 'Cycles Algébriques; Aspects Transcendents, Grenoble 2001'. The topics range from introductory lectures on algebraic cycles to more advanced material. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. Among the topics treated are: cycle spaces, Chow topology, morphic cohomology, Grothendieck motives, Chow-Künneth decompositions of the diagonal, motivic cohomology via higher Chow groups, the Hodge conjecture for certain fourfolds, an effective version of Nori's connectivity theorem, Beilinson's Hodge and Tate conjecture for open complete intersections. As the lectures were intended for non-specialists many examples have been included to illustrate the theory. As such this book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

    • Designed for non-specialists with lots of illustrative examples
    • Contains introductory material as well as advanced topics, ideal for those entering the field
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    Product details

    • Date Published: April 2004
    • format: Paperback
    • isbn: 9780521545471
    • length: 310 pages
    • dimensions: 228 x 153 x 18 mm
    • weight: 0.42kg
    • contains: 1 b/w illus.
    • availability: In stock
  • Table of Contents

    Part I. Introductory Material:
    1. Chow varieties, the Euler-Chow series and the total coordinate ring J. Elizondo
    2. Introduction to Lawson homology C. Peters and S. Kosarew
    Part II. Lawson (Co)homology:
    3. Topological properties of the algebraic cycles functor P. Lima-Filho
    Part III. Motives and Motivic Cohomology:
    4. Lectures on motives J. P. Murre
    5. A short introduction to higher Chow groups P. Elbaz-Vincent
    Part IV. Hodge Theoretic Invariants of Cycles:
    6. Three lectures on the Hodge conjecture J. D. Lewis
    7. Lectures on Nori's connectivity theorem J. Nagel
    8. Beilinson's Hodge and Tate conjectures S. Saito.

  • Editors

    S. Müller-Stach, Johannes Gutenberg Universität Mainz, Germany

    C. Peters, Université de Grenoble


    J. Elizondo, C. Peters, S. Kosarew, P. Lima-Filho, J. P. Murre, P. Elbaz-Vincent, J. D. Lewis, J. Nagel, S. Saito

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