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Lectures on the Theory of Pure Motives

Jacob P. Murre Universiteit Leiden, Leiden, The Netherlands
Jan Nagel Université de Bourgogne, Dijon Cedex, France
Chris A. M. Peters Université Grenoble I, St. Martin d’Heres, France
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Softcover ISBN: 978-0-8218-9434-7
Product Code: ULECT/61
List Price: $47.00 MAA Member Price:$42.30
AMS Member Price: $37.60 Electronic ISBN: 978-1-4704-1039-1 Product Code: ULECT/61.E List Price:$44.00
MAA Member Price: $39.60 AMS Member Price:$35.20
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AMS Member Price: $56.40 Click above image for expanded view Lectures on the Theory of Pure Motives Jacob P. Murre Universiteit Leiden, Leiden, The Netherlands Jan Nagel Université de Bourgogne, Dijon Cedex, France Chris A. M. Peters Université Grenoble I, St. Martin d’Heres, France Available Formats:  Softcover ISBN: 978-0-8218-9434-7 Product Code: ULECT/61  List Price:$47.00 MAA Member Price: $42.30 AMS Member Price:$37.60
 Electronic ISBN: 978-1-4704-1039-1 Product Code: ULECT/61.E
 List Price: $44.00 MAA Member Price:$39.60 AMS Member Price: $35.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$70.50 MAA Member Price: $63.45 AMS Member Price:$56.40
• Book Details

University Lecture Series
Volume: 612013; 149 pp
MSC: Primary 14; 19;

The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to have a number of additional properties predicted by Grothendieck's standard conjectures, but these conjectures remain wide open. The theory for mixed motives is still incomplete.

This book deals primarily with the theory of pure motives. The exposition begins with the fundamentals: Grothendieck's construction of the category of pure motives and examples. Next, the standard conjectures and the famous theorem of Jannsen on the category of the numerical motives are discussed. Following this, the important theory of finite dimensionality is covered. The concept of Chow-Künneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of Bloch-Beilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives.

Readership

Graduate students and research mathematicians interested in algebraic cycles and motives.

• Table of Contents

• Chapters
• Chapter 1. Algebraic cycles and equivalence relations
• Appendix A. Survey of some of the main results on Chow groups
• Appendix B. Proof of the theorem of Voisin-Voevodsky
• Chapter 2. Motives: Construction and first properties
• Chapter 3. On Grothendieck’s standard conjectures
• Chapter 4. Finite dimensionality of motives
• Chapter 5. Properties of finite dimensional motives
• Chapter 6. Chow-Künneth decomposition; The Picard and Albanese motive
• Appendix C. Chow-Künneth decomposition in a special case
• Chapter 7. On the conjectural Bloch-Beilinson filtration
• Chapter 8. Relative Chow-Künneth decomposition
• Appendix D. Surfaces fibered over a curve
• Chapter 9. Beyond pure motives
• Appendix E. The category of motivic complexes
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Volume: 612013; 149 pp
MSC: Primary 14; 19;

The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to have a number of additional properties predicted by Grothendieck's standard conjectures, but these conjectures remain wide open. The theory for mixed motives is still incomplete.

This book deals primarily with the theory of pure motives. The exposition begins with the fundamentals: Grothendieck's construction of the category of pure motives and examples. Next, the standard conjectures and the famous theorem of Jannsen on the category of the numerical motives are discussed. Following this, the important theory of finite dimensionality is covered. The concept of Chow-Künneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of Bloch-Beilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives.

Readership

Graduate students and research mathematicians interested in algebraic cycles and motives.

• Chapters
• Chapter 1. Algebraic cycles and equivalence relations
• Appendix A. Survey of some of the main results on Chow groups
• Appendix B. Proof of the theorem of Voisin-Voevodsky
• Chapter 2. Motives: Construction and first properties
• Chapter 3. On Grothendieck’s standard conjectures
• Chapter 4. Finite dimensionality of motives
• Chapter 5. Properties of finite dimensional motives
• Chapter 6. Chow-Künneth decomposition; The Picard and Albanese motive
• Appendix C. Chow-Künneth decomposition in a special case
• Chapter 7. On the conjectural Bloch-Beilinson filtration
• Chapter 8. Relative Chow-Künneth decomposition
• Appendix D. Surfaces fibered over a curve
• Chapter 9. Beyond pure motives
• Appendix E. The category of motivic complexes
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