2013/07/11 by Isamu Iwanari, Iwanari, Isamu · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1307.3175
openalex publication_date 2013/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the symmetric monoidal category of mixed motives generated by an abelian variety (more generally, an abelian scheme) can be described as a certain module category. More precisely, we describe it as the category of quasi-coherent complexes over a derived quotient stack constructed from a motivic algebra of the abelian variety. We then study the structure of the motivic Galois groups of their mixed motives. We prove that the motivic Galois group is decomposed into a unipotent part constructed from the motivic algebra, and the reductive quotient which is the Tannaka dual of Grothendieck numerical motives.