The Arithmetic and Geometry of Algebraic Cycles (NATO Science Series C: (closed)) [Paperback]

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

Book Description

Publication Date: February 29, 2000 | ISBN-10: 0792361946 | ISBN-13: 978-0792361947 | Edition: 1

The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.

Product Details

• Paperback: 648 pages
• Publisher: Springer; 1 edition (February 29, 2000)
• Language: English
• ISBN-10: 0792361946
• ISBN-13: 978-0792361947
• Product Dimensions: 9.2 x 6.2 x 1.5 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #5,005,393 in Books (See Top 100 in Books)

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5.0 out of 5 stars collection of surveys, February 20, 2004

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This review is from: The Arithmetic and Geometry of Algebraic Cycles (NATO Science Series C: (closed)) (Hardcover)

This book is a collection of survey articles on the subject of algebraic cycles and motivic cohomology based on the NATO conference on algebraic cycles held at Banff, Canada. Survey papers contained in this book will definitely tell you what you need to know and where you should go to pursue research in this area. Libraries in major universities will definitely have this very important collection, but, if for algebraic geometers who work on algebraic cycles, having this book can be very convenient for their personal usage.