Explicit generators for (conjectural) mixed motives (in Voevodsky's $\dmge$). The Kunneth decomposition of pure (numerical) motives

Details Explicit generators for (conjectural) mixed motives (in Voevodsky's $\dmge$). The Kunneth decomposition of pure (numerical) motives Explicit generators for (conjectural) mixed motives (in Voevodsky's $\dmge$). The Kunneth decomposition of pure (numerical) motives

2007-03-17

arxiv.org/abs/math/0703499v2

Mathematics

Algebraic Geometry

New very explicit mixed (conjecturally) motives in Voevodsky's $DM$!

Scientific paper

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 $P$.

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