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

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 false{Frfalse}r≥0 of Suslin's singular homology group, H0singfalse(Gfalse), such that the successive quotients are isomorphic to a certain Somekawa K‐group.