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arXiv · 1704.04282

Action of Correspondences on Filtrations on Cohomology and 0-cycles of Abelian Varieties

Rakesh Pawar
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Abstract

We prove that, given a symmetrically distinguished correspondence of a suitable complex abelian variety (which include any abelian variety of dimension atmost 5, powers of complex elliptic curves, etc.) which vanishes as a morphism on a certain quotient of its middle singular cohomology, then it vanishes as a morphism on the deepest part of a particular filtration on the Chow group of 0-cycles of the abelian variety. As a consequence, we prove that given an automorphism of such an abelian variety, which acts as the identity on a certain quotient of its middle singular cohomology, then it acts as the identity on the deepest part of this filtration on the Chow group of 0-cycles of the abelian variety. As an application, we prove that for the Generalized Kummer variety associated to a complex abelian surface and the automorphism induced from a symplectic automorphism of the complex abelian surface, the automorphism of the Generalized Kummer variety acts as the identity on a certain subgroup of its Chow group of 0-cycles.

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Rakesh Pawar. 2017-04-13. Action of Correspondences on Filtrations on Cohomology and 0-cycles of Abelian Varieties. https://arxiv.org/abs/1704.04282

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