Transcendental Aspects of Algebraic Cycles
Proceedings of the Grenoble Summer School, 2001

Lecture notes for graduates or researchers wishing to enter this modern field of research.

S. Müller-Stach (Edited by), C. Peters (Edited by)

9780521545471, Cambridge University Press

Paperback, published 20 April 2004

310 pages, 1 b/w illus.
22.8 x 15.3 x 1.8 cm, 0.42 kg

This is a collection of lecture notes from the Summer School 'Cycles Algébriques; Aspects Transcendents, Grenoble 2001'. The topics range from introductory lectures on algebraic cycles to more advanced material. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. Among the topics treated are: cycle spaces, Chow topology, morphic cohomology, Grothendieck motives, Chow-Künneth decompositions of the diagonal, motivic cohomology via higher Chow groups, the Hodge conjecture for certain fourfolds, an effective version of Nori's connectivity theorem, Beilinson's Hodge and Tate conjecture for open complete intersections. As the lectures were intended for non-specialists many examples have been included to illustrate the theory. As such this book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

Part I. Introductory Material: 1. Chow varieties, the Euler-Chow series and the total coordinate ring J. Elizondo
2. Introduction to Lawson homology C. Peters and S. Kosarew
Part II. Lawson (Co)homology: 3. Topological properties of the algebraic cycles functor P. Lima-Filho
Part III. Motives and Motivic Cohomology: 4. Lectures on motives J. P. Murre
5. A short introduction to higher Chow groups P. Elbaz-Vincent
Part IV. Hodge Theoretic Invariants of Cycles: 6. Three lectures on the Hodge conjecture J. D. Lewis
7. Lectures on Nori's connectivity theorem J. Nagel
8. Beilinson's Hodge and Tate conjectures S. Saito.

Subject Areas: Topology [PBP], Geometry [PBM], Number theory [PBH], Algebra [PBF]