Algebraic Cycles and Motives: Volume 2

A self-contained account of the subject of algebraic cycles and motives as it stands.

Jan Nagel (Edited by), Chris Peters (Edited by)

9780521701754, Cambridge University Press

Paperback, published 3 May 2007

374 pages, 5 b/w illus. 6 tables
22.9 x 15.2 x 2.1 cm, 0.61 kg

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.

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.

Subject Areas: Applied mathematics [PBW], Topology [PBP], Geometry [PBM]