The Arithmetic and Geometry of Algebraic Cycles

1. Front Matter

   Pages i-xxx

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2. Cohomological Methods

   1. Front Matter

      Pages 1-1

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   2. Lectures on Algebro-Geometric Chern-Weil and Cheeger-Chern-Simons Theory for Vector Bundles

      • Spencer Bloch, Hélène Esnault

      Pages 3-28

   3. Deligne Cohomology and the Geometric (Co-)Bar Constructions

      • Paweł Gajer

      Pages 29-50

   4. Kuga-Satake Varieties and the Hodge Conjecture

      • Bert van Geemen

      Pages 51-82

   5. Hodge and Well Classes on Abelian Varieties

      • V. Kumar Murty

      Pages 83-115

   6. Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients

      • Andrei Suslin, Vladimir Voevodsky

      Pages 117-189

3. Chow Groups and Motives

   1. Front Matter

      Pages 191-191

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   2. Indecomposable Higher Chow Cycles

      • B. Brent Gordon, James D. Lewis

      Pages 193-224

   3. Equivalence Relations on Algebraic Cycles

      • Uwe Jannsen

      Pages 225-260

   4. Letter from Jannsen to Gross on higher Abel-Jacobi maps

      • B. Brent Gordon, James D. Lewis, Stefan Müller-Stach, Shuji Saito, Noriko Yui

      Pages 261-275

   5. Finiteness of Torsion in the Codimension-Two Chow Group: An Axiomatic Approach

      • Andreas Langer

      Pages 277-284

   6. Algebraic Cycle Complexes

      • Stefan Müller-Stach

      Pages 285-305

   7. Algebraic Cycles on Abelian Varieties

      • J. P. Murre

      Pages 307-320

   8. Motives and Filtrations on Chow Groups, II

      • Shuji Saito

      Pages 321-346

   9. Zero Cycles on Singular Varieties

      • V. Srinivas

      Pages 347-382

4. Arithmetic Methods

   1. Front Matter

      Pages 383-383

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   2. Prepotentials of Yukawa Couplings of Certain Calabi-Yau 3-Folds and Mirror Symmetry

      • Masa-Hiko Saito

      Pages 385-425

   3. Weight-Monodromy Conjecture for ℓ-Adic Representations Associated to Modular Forms

      • Takeshi Saito

      Pages 427-431

   4. Cohomology Computations Related to the ι-Adic Abel-Jacobi Map Modulo ι

      • Chad Schoen

      Pages 433-466

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.

• Abelian variety
• Dimension
• Grad
• K-theory
• algebraic geometry

• University of Oklahoma, Norman, USA

  B. Brent Gordon

• University of Alberta, Edmonton, Canada

  James D. Lewis

• Universität-GH-Essen, Essen, Germany

  Stefan Müller-Stach

• Tokyo Institute of Technology, Tokyo, Japan

  Shuji Saito

• Queen’s University, Kingston, Canada

  Noriko Yui

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