Vol 9. The Geometry of Algebraic Cycles

The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.

Contents

Transcendental aspects

• The Hodge theoretic fundamental group and its cohomology 
  D. Arapura
• The real regulator for a self-product of a general surface 
  X. Chen and J. D. Lewis
• Lipschitz cocycles and Poincaré duality 
  E. M. Friedlander and C. Haesemeyer
• On the motive of a K3 surface 
  C. Pedrini
• Two observations about normal functions 
  C. Schnell

Positive characteristics and arithmetic

• Autour de la conjecture de Tate à coefficients Z_l pour les variétés sur les corps finis 
  J. L. Colliot-Théléne and T. Szamuely
• Regulators via iterated integrals (numerical computations) 
  H. Gangl
• Zero-cycles on algebraic tori 
  A. S. Merkurjev
• Chow-Künneth projectors and l-adic cohomology 
  A. Miller

Connections with mathematical physics

• Motives associated to sums of graphs 
  S. Bloch
• Double shuffle relations and renormalization of multiple zeta values 
  L. Guo, S. Paycha, B. Xie, and B. Zhan