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

doi:10.1017/CBO9780511734984

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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Contents

Frontmatter
pp i-iv
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Contents
pp v-vii
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List of participants
pp viii-x
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Preface
pp xi-xviii
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Acknowledgements
pp xix-xx
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Part I - Introductory material
pp 1-2
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1 - Chow varieties, the Euler–Chow series and the total coordinate ring
pp 3-43
- By E. Javier Elizondo, Instituto de Matemáticas, Ciudad Universitaria, UNAM, México DF 04510, Mexico
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2 - Introduction to Lawson homology
pp 44-72
- By Chris Peters, Department of Mathematics, University of Grenoble I, UMR 5582 CNRS-UJF, 38402 Saint-Martin d'Hères, France, Siegmund Kosarew, Department of Mathematics, University of Grenoble I, UMR 5582 CNRS-UJF, 38402 Saint-Martin d'Hères, France
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Part II - Lawson (co)homology
pp 73-74
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3 - Topological properties of the algebraic cycles functor
pp 75-120
- By Paulo Lima-Filho, Department of Mathematics, Texas A&M University, College Station, TX 77840, USA
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Part III - Motives and motivic cohomology
pp 121-122
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4 - Lectures on motives
pp 123-170
- By Jacob P. Murre, Department of Mathematics, University of Leiden, Niels Bohrweg 1, P.O. Box 9512, 2300 RA Leiden, The Netherlands
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5 - A short introduction to higher Chow groups
pp 171-196
- By Philippe Elbaz-Vincent, Institut de Mathématiques et Modélisation de Montpellier, UMR CNRS 5030, CC 51, Université Montpellier II, 34095 Montpellier Cedex 5, France
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Part IV - Hodge theoretic invariants of cycles
pp 197-198
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6 - Three lectures on the Hodge conjecture
pp 199-234
- By James D. Lewis, Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
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7 - Lectures on Nori's connectivity theorem
pp 235-275
- By J. Nagel, Université Lille 1, Mathématiques, Bâtiment MZ, 596SS Villeneuve d'Ascq Cedex, France
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8 - Beilinson's Hodge and Tate conjectures
pp 276-290
- By Shuji Saito, University of Nagano
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Transcendental Aspects of Algebraic Cycles

Proceedings of the Grenoble Summer School, 2001

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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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