Overview

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.

Full Product Details

Author:   Jan Nagel (Université de Lille) ,  Chris Peters (Université Joseph Fourier, Grenoble)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   344
ISBN:  

9781107325968

ISBN 10:   110732596
Publication Date:   05 April 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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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.

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Author Information

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.

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