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Lectures on the Theory of Pure Motives
About this Title
Jacob P. Murre, Universiteit Leiden, Leiden, The Netherlands, Jan Nagel, Université de Bourgogne, Dijon Cedex, France and Chris A. M. Peters, Université Grenoble I, St. Martin d’Heres, France
Publication: University Lecture Series
Publication Year:
2013; Volume 61
ISBNs: 978-0-8218-9434-7 (print); 978-1-4704-1039-1 (online)
DOI: https://doi.org/10.1090/ulect/061
MathSciNet review: MR3052734
MSC: Primary 14-02; Secondary 14C15, 14C25, 19E15
Table of Contents
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Front/Back Matter
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