Algebraic cycles and motives

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Algebraic cycles and motives

edited by Jan Nagel, Chris Peters

（London Mathematical Society lecture note series, 343-344）

Cambridge University Press, 2007

  • v. 1 : pbk
  • v. 2 : pbk

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Includes bibliographical references

Description and Table of Contents

Volume

v. 1 : pbk ISBN 9780521701747

Description

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 2007 book is one of two volumes that provide a self-contained account of the subject. 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.

Table of Contents

  • Foreword
  • Part I. Survey Articles: 1. The motivic vanishing cycles and the conservation conjecture J. Ayoub
  • 2. On the theory of 1-motives L. Barbieri-Viale
  • 3. Motivic decomposition for resolutions of threefolds M. de Cataldo and L. Migliorini
  • 4. Correspondences and transfers F. Deglise
  • 5. Algebraic cycles and singularities of normal functions M. Green and Ph. Griffiths
  • 6. Zero cycles on singular varieties A. Krishna and V. Srinivas
  • 7. Modular curves, modular surfaces and modular fourfolds D. Ramakrishnan.
Volume

v. 2 : pbk ISBN 9780521701754

Description

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.

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. Kunneth 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. Muller-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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