On the Motive of a Commutative Algebraic Group

We prove a canonical Künneth decomposition for the motive of a commutative group scheme over a field. Moreover, we show that this decomposition behaves under the group law just as in cohomology. We also deduce applications of the decomposition to the existence of a weight filtration, computation of any Weil cohomology theory and study of 1-motives.

2010 Mathematics Subject Classification: 14C15 (primary), 14L10, 19E15, 14F20, 14K99 (secondary)

Keywords and Phrases: Voevodsky motives, semiabelian varieties, Künneth decomposition, 1-motives, Kimura finiteness

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