Mixed motives and quotient stacks: Abelian varieties

Isamu Iwanari

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arXiv · 1307.3175

Mixed motives and quotient stacks: Abelian varieties

Isamu Iwanari

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Abstract

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.

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BibTeX RIS

Isamu Iwanari. 2013-07-11. Mixed motives and quotient stacks: Abelian varieties. https://arxiv.org/abs/1307.3175

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