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Transcendental Aspects of Algebraic Cycles S. Muller-Stach (Johannes Gutenberg Universitat Mainz, Germany)

Transcendental Aspects of Algebraic Cycles By S. Muller-Stach (Johannes Gutenberg Universitat Mainz, Germany)

Transcendental Aspects of Algebraic Cycles by S. Muller-Stach (Johannes Gutenberg Universitat Mainz, Germany)


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Summary

This is a collection of lecture notes from the Summer School 'Cycles Algebriques; Aspects Transcendents, Grenoble 2001'. The lectures were intended for non-specialists so include many illustrative examples. This book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

Transcendental Aspects of Algebraic Cycles Summary

Transcendental Aspects of Algebraic Cycles: Proceedings of the Grenoble Summer School, 2001 by S. Muller-Stach (Johannes Gutenberg Universitat Mainz, Germany)

This is a collection of lecture notes from the Summer School 'Cycles Algebriques; 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-Kunneth 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.

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.

Additional information

NLS9780521545471
9780521545471
0521545471
Transcendental Aspects of Algebraic Cycles: Proceedings of the Grenoble Summer School, 2001 by S. Muller-Stach (Johannes Gutenberg Universitat Mainz, Germany)
New
Paperback
Cambridge University Press
2004-04-20
310
N/A
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