Tate traces and classification of Chow motives

This talk is based on a joint work with Charles De Clercq. The main result is a classification theorem for some Chow motives with finite coefficients, which applies, notably, to motives of projective homogeneous varieties under some semi-simple algebraic groups. The result uses a new invariant, the Tate trace of a motive, defined as a pure Tate summand of maximal rank. If time permits, the notion of critical variety will be presented, as an application of our result.