University of Cambridge > Talks.cam > Algebraic Geometry Seminar > On the Chow group and the motive of a commutative algebraic group

On the Chow group and the motive of a commutative algebraic group

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A classical result of Beauville shows that the action of the multiplication by n on the Chow group of an abelian variety is semisimple with finite explicit eigenvalues. This result was used by Deninger and Murre to show that the Chow motive of an abelian variety has a canonical Künneth decomposition. We will show that both results generalize to semiabelian varieties (or more generally to commutative algebraic groups). The method is different and the logical dependence changes: we will directly work with the motive and then deduce the result on the Chow group. In the talk we will recall generalities on Voevodsky’s motives, as well as several of their arithmetic and geometric applications. This is a joint work with Steven Enright-Ward and Annette Huber.

This talk is part of the Algebraic Geometry Seminar series.

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