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arXiv · 1901.04590

A filtration on the higher Chow group of zero cycles on an abelian variety

Buntaro Kakinoki
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Abstract

In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are connected to the Somekawa type $K$-group. Via the \'{e}tale cycle map, we will compare this filtration with a filtration on the \'{e}tale cohomology induced by the Hochschild-Serre spectral sequence. As an application over local fields, we obtain an estimate of the kernel of the reciprocity map.

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Buntaro Kakinoki. 2019-01-14. A filtration on the higher Chow group of zero cycles on an abelian variety. https://arxiv.org/abs/1901.04590

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