Synopses & Reviews
Algebraic cycles and motives is a subfield of pure mathematics which has attracted much attention since the pioneering work of A. Grothendieck on motives. The EAGER conference 'Algebraic Cycles and Motives' was held in Leiden on the occasion of Professor J. P. Murre's 75th birthday in September 2004 and was attended by many of the leading experts in the field. This two volume book presents twenty-two selected papers from the international conference. Both survey and research articles are included, covering main research topics and interesting new results. Topics discussed include the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers andstudents in complex algebraic geometry and arithmetic geometry will find this two volume book presents a self-contained account of this subject as it stands today.
Synopsis
Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This book is one of two volumes that provide a self-contained account of the subject as it stands. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.
Synopsis
A self-contained account of the subject of algebraic cycles and motives as it stands.
Synopsis
These two volumes provide a self-contained account of research on algebraic cycles and motives. Twenty-two contributions from leading figures survey the key research strands, including: Abel-Jacobi/regulator maps and normal functions; Voevodsky's triangulated category of mixed motives; conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups.
About the Author
Jan Nagel is a Lecturer at UFR de Mathématiques Pures et Appliquées, Université Lille 1.Chris Peters is a Professor at Institut Fourier, Université Grenoble 1.
Table of Contents
Part II. Research Articles: 8. Beilinson's Hodge conjecture with coefficients M. Asakura and S. Saito; 9. On the splitting of the Bloch-Beilinson filtration A. Beauville; 10. Künneth projectors S. Bloch and H. Esnault; 11. The Brill-Noether curve of a stable bundle on a genus two curve S. Brivio and A. Verra; 12. On Tannaka duality for vector bundles on p-adic curves C. Deninger and A. Werner; 13. On finite-dimensional motives and Murre's conjecture U. Jannsen; 14. On the transcendental part of the motive of a surface B. Kahn, J. P. Murre and C. Pedrini; 15. A note on finite dimensional motives S. I. Kimura; 16. Real regulators on Milnor complexes, II J. D. Lewis; 17. Motives for Picard modular surfaces A. Miller, S. Müller-Stach, S. Wortmann, Y.-H.Yang, K. Zuo; 18. The regulator map for complete intersections J. Nagel; 19. Hodge number polynomials for nearby and vanishing cohomology C. Peters and J. Steenbrink; 20. Direct image of logarithmic complexes M. Saito; 21. Mordell-Weil lattices of certain elliptic K3's T. Shioda; 22. Motives from diffraction J. Stienstra.