The Arithmetic and Geometry of Algebraic Cycles

Description

The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al­ berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec­ tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic­ ipants. In addition, participants' reprints and preprints were displayed through­ out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction Front Matter....Pages i-xxx Front Matter....Pages 1-1 Lectures on Algebro-Geometric Chern-Weil and Cheeger-Chern-Simons Theory for Vector Bundles....Pages 3-28 Deligne Cohomology and the Geometric (Co-)Bar Constructions....Pages 29-50 Kuga-Satake Varieties and the Hodge Conjecture....Pages 51-82 Hodge and Well Classes on Abelian Varieties....Pages 83-115 Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients....Pages 117-189 Front Matter....Pages 191-191 Indecomposable Higher Chow Cycles....Pages 193-224 Equivalence Relations on Algebraic Cycles....Pages 225-260 Letter from Jannsen to Gross on higher Abel-Jacobi maps....Pages 261-275 Finiteness of Torsion in the Codimension-Two Chow Group: An Axiomatic Approach....Pages 277-284 Algebraic Cycle Complexes....Pages 285-305 Algebraic Cycles on Abelian Varieties....Pages 307-320 Motives and Filtrations on Chow Groups, II....Pages 321-346 Zero Cycles on Singular Varieties....Pages 347-382 Front Matter....Pages 383-383 Prepotentials of Yukawa Couplings of Certain Calabi-Yau 3-Folds and Mirror Symmetry....Pages 385-425 Weight-Monodromy Conjecture for ℓ-Adic Representations Associated to Modular Forms....Pages 427-431 Cohomology Computations Related to the ι -Adic Abel-Jacobi Map Modulo ι ....Pages 433-466 Integral Elements in K -Theory and Products of Modular Curves....Pages 467-489 Appendix to the Paper of Scholl....Pages 491-493 Reduction of Abelian Varieties....Pages 495-513 The Arithmetic of Certain Calabi-Yau Varieties over Number Fields....Pages 515-560 Front Matter....Pages 383-383 Classical and Elliptic Polylogarithms and Special Values of L-Series....Pages 561-615