Non-Fiction Books:

The Arithmetic and Geometry of Algebraic Cycles

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Hardback
$586.00
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Description

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 in the late 1990s, 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 text 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.
Release date NZ
February 29th, 2000
Audiences
  • Postgraduate, Research & Scholarly
  • Professional & Vocational
Contributors
  • Edited by B.Brent Gordon
  • Edited by James D. Lewis
  • Edited by Noriko Yui
  • Edited by Shuji Saito
  • Edited by Stefan Muller-Stach
Illustrations
XXX, 615 p.
Pages
615
Dimensions
155x235x34
ISBN-13
9780792361930
Product ID
2823366

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