Relations between the Chow motive and the noncommutative motive of a smooth projective variety

Marcello Bernardara (1) , Goncalo Tabuada (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MIT - Massachusetts Institute of Technology

In this note we relate the notions of Lefschetz type, decomposability, and isomorphism, on Chow motives with the notions of unit type, decomposability, and isomorphism, on noncommutative motives. Some examples, counter-examples, and applications are also described.

Mots clés: semi-ortogonal decompositions; quadratic forms; Severi-Brauer varieties.; Severi-Brauer varieties; Motivic decompositions; Chow motives; noncommutative motives; full exceptional collections

Domaines: Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; K-théorie et homologie [math.KT]

Marcello Bernardara, Goncalo Tabuada. Relations between the Chow motive and the noncommutative motive of a smooth projective variety. Journal of Pure and Applied Algebra, 2015. ⟨hal-00876533⟩