Some results about zero‐cycles on abelian and semi‐abelian varieties

Evangelia Gazaki

Mathematische Nachrichten, 2019, vol. 292, issue 8, 1716-1726

Abstract: In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of Qp with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration {Fr}r≥0 of Suslin's singular homology group, H0sing(G), such that the successive quotients are isomorphic to a certain Somekawa K‐group.

Date: 2019
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