Lectures on the Theory of Pure Motives

Murre, Nagle, and Peters begin by outlining algebraic cycles and Chow groups, which are at the heart of the theory of pure motives created by A. Grothendieck beginning about 1964. They continue with discussions of construction and first properties of motives, Grothendieck's standard conjectures, the finite dimensionality of motives, properties of finite dimensional motives, Chow-Künneth decomposition and the Picard and Albamese motive, the conjectural Bloch-Beilinson filtration, relative Chow-Künneth decomposition, and beyond pure motives. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)