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

2007/03/17 by Mikhail V. Bondarko, Bondarko, M. V.
Mathematics · #14F25 #14F40 #14F42 #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0703499

openalex publication_date 2007/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we describe very explicitly a rich family of mixed motives that generates Voevodsky's DM^eff_gmℚ (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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