Abstract: Motivic decompositions of projective varieties in the category
of Chow motives are very useful to study the geometry of varieties. I will
talk about the paper https://arxiv.org/pdf/2302.12311.pdf where the
authors define a new motivic invariant called the Tate trace of a motive
and use it to classify motives of projective homogenous varieites with
finite coefficients. It is also shown that the techniques can be used to
characterise motivic equivalence of semisimple groups through Tits
indices.
|