numerical motive

A pure motive defined by applying numerical equivalence of algebraic cycles.

The category of numerical motives is a semisimple abelian category.

In fact, numerical equivalence is precisely the only adequate equivalence relation relation that gives the category of pure motives this property.

A standard account is in

- U. Jannsen, S. Kleiman and J.-P. Serre,
*Motives*, Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington, Seattle, Washington, July 20â€“August 2, 1991. Proceedings of Symposia in Pure Mathematics 55, part 1 and 2. American Mathematical Society, Providence, RI, 1994.

The fact that the category of numerical motives is semisimple abelian is in

- Uwe Jannsen,
*Motives, numerical equivalence, and semi-simplicity*, Invent. math. 107 (1992) (pdf)

A brief review of numerical noncommutative motives is in section 4 of

- Goncalo Tabuada,
*A guided tour through the garden of noncommutative motives*, (arxiv1108.3787);

Revised on June 13, 2013 01:29:44
by Urs Schreiber
(131.174.43.123)