Algebraic Cycles and Motives: Volume 2 (London Mathematical Society Lecture Note Series, Series Number 344)

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. Contents Preface Volume 2: Research Articles 1. Beilinson's Hodge conjecture with coefficients 2. On the splitting of the Bloch-Beilinson filtration 3. Künneth projectors 4. The Brill-Noether curve of a stable bundle on a genus two curve 5. On Tannaka duality for vector bundles on p-adic curves 6. On finite-dimensional motives and Murre's conjecture 7. On the transcendental part of the motive of a surface 8. A note on finite dimensional motives 9. Real regulators on Milnor complexes, II 10. Chow-Künneth decomposition for universal families over Picard modular surfaces 11. The regulator map for complete intersections 12. Hodge number polynomials for nearby and vanishing cohomology 13. Direct image of logarithmic complexes 14. Correspondence of elliptic curves and Mordell-Weil lattices of certain elliptic K3's 15. Motives from diffraction 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.