Chow motives versus non-commutative motives

2011/03/01 by Tabuada, Goncalo
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1103.0200

Abstract

In this article we formalize and enhance Kontsevich's beautiful insight that Chow motives can be embedded into non-commutative ones after factoring out by the action of the Tate object. We illustrate the potential of this result by developing three of its manyfold applications: (1) the notions of Schur and Kimura finiteness admit an adequate extension to the realm of non-commutative motives; (2) Gillet-Soule's motivic measure admits an extension to the Grothendieck ring of non-commutative motives; (3) certain motivic zeta functions admit an intrinsic construction inside the category of non-commutative motives.

Related

• Relations between the Chow motive and the noncommutative motive of a smooth projective variety
• Noncommutative motives and their applications
• Noncommutative motives, numerical equivalence, and semi-simplicity
• Abelian motives and Shimura varieties in nonzero characteristic
• Weight structure on noncommutative motives