The Arithmetic and Geometry of Algebraic Cycles

Cohomological Methods.- Lectures on algebro-geometric Chern-Weil and Cheeger-Chern-Simons theory for vector bundles.- Deligne cohomology and the geometric (co)bar constructions.- Kunga-Satake varieties and the Hodge conjecture.- Hodge and Weil classes on abelian varieties.- Bloch-Kato conjecture and motivic cohomology with finite coefficients 117.- Chow Groups and Motives.- Indecomposable hogher Chow cycles.- Equivalence relations on algebraic cycles.- Letter to Dick Gross on higher Abel-Jacobi maps.- Finiteness of torsion in the codimension-two Chow group: An Axiomatic Approach.- Algebraic cycle complexes: Basic Properties.- Algebraic cycles on abelian varieties: Application of abstract Fourier theory.- Motives and filtrations on Chow groups II.- Zero cycles on singular varieties.- Arithmetic Methods.- Prepotentials of Yukawa couplings of certain Calabi-Yau 3-folds and mirror symmetry.- Weight-monodromy conjecture for 1-adic representations associated to modular forms: A supplement to the paper [10].- Cohomology computations related to the 1-adic Abel-Jacobi map modulo l.- Integral elements in K-theory and products of modular curves.- Appendix to Scholl’s article: A counterexample to a conjecture of Beilinson.- Reduction of abelian varieties.- The arithmetic of cetain Calabi-Yau varieties over number fields.- Classical and elliptic polylogarithms and special values of L-series.