Transcendental Aspects of Algebraic Cycles
Proceedings of the Grenoble Summer School, 2001
1st Edition
Published on 19. January 2011
978-0-511-89397-1 (ISBN)
Description
This is a collection of lecture notes from the Summer School 'Cycles Algebriques; 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-Kuenneth 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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 1 Halftones, unspecified
File size
2,08 MB
ISBN-13
978-0-511-89397-1 (9780511893971)
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Schweitzer Classification
Other editions
Additional editions
S. Mueller-Stach | C. Peters
Transcendental Aspects of Algebraic Cycles
Proceedings of the Grenoble Summer School, 2001
Book
04/2004
Cambridge University Press
€86.10
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Persons
Content
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.
