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The Arithmetic and Geometry of Algebraic Cycles
B. Brent Gordon
James D. Lewis
Stefan Müller-Stach
Shuji Saito
Noriko Yui
出版
Springer Science & Business Media
, 2000-02-29
主題
Mathematics / Algebra / General
Mathematics / Algebra / Abstract
Mathematics / Applied
Mathematics / Calculus
Mathematics / Geometry / Algebraic
Mathematics / Mathematical Analysis
Mathematics / Topology
Mathematics / Numerical Analysis
ISBN
0792361946
9780792361947
URL
http://books.google.com.hk/books?id=pV8KjZ-qB60C&hl=&source=gbs_api
EBook
SAMPLE
註釋
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.