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

doi:10.1017/CBO9780511734984

Transcendental Aspects of Algebraic Cycles

Proceedings of the Grenoble Summer School, 2001

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Bouali, Johann 2016. Motives of quadric bundles. Manuscripta Mathematica, Vol. 149, Issue. 3-4, p. 347.

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Edited by S. Müller-Stach, Johannes Gutenberg Universität Mainz, Germany, C. Peters, Université de Grenoble

Publisher:: Cambridge University Press
Online publication date:: May 2010
Print publication year:: 2004
Online ISBN:: 9780511734984
DOI:: https://doi.org/10.1017/CBO9780511734984

Subjects:: Mathematics (general), Mathematics, Real and Complex Analysis, Number Theory
Series:: London Mathematical Society Lecture Note Series (313)

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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.

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Transcendental Aspects of Algebraic Cycles

Proceedings of the Grenoble Summer School, 2001

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-vii

List of participants
pp viii-x

Preface
pp xi-xviii

Acknowledgements
pp xix-xx

Part I - Introductory material
pp 1-2

1 - Chow varieties, the Euler–Chow series and the total coordinate ring
pp 3-43

2 - Introduction to Lawson homology
pp 44-72

Part II - Lawson (co)homology
pp 73-74

3 - Topological properties of the algebraic cycles functor
pp 75-120

Part III - Motives and motivic cohomology
pp 121-122

4 - Lectures on motives
pp 123-170

5 - A short introduction to higher Chow groups
pp 171-196

Part IV - Hodge theoretic invariants of cycles
pp 197-198

6 - Three lectures on the Hodge conjecture
pp 199-234

7 - Lectures on Nori's connectivity theorem
pp 235-275

8 - Beilinson's Hodge and Tate conjectures
pp 276-290

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Transcendental Aspects of Algebraic Cycles

Proceedings of the Grenoble Summer School, 2001

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