Explicit generators for (conjectural) mixed motives (in Voevodsky's $\dmge$). The Kunneth decomposition of pure (numerical) motives
Abstract
Description
In this note we describe very explicitly a rich family of mixed motives that generates Voevodsky's $DM^{eff}_{gm}{\mathbb{Q}}$ (as a triangulated category). They "should be" mixed since they have only one non-zero Betti cohomology group. Our method also allows to define a family of direct summands of the numerical motif of any smooth projective variety $P$. Modulo certain standard conjectures, this construction yields the Kunneth decomposition of the diagonal of $P$.
New very explicit mixed (conjecturally) motives in Voevodsky's $DM$!
New very explicit mixed (conjecturally) motives in Voevodsky's $DM$!