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2020 A filtration on the higher Chow group of zero cycles on an abelian variety
Buntaro Kakinoki
Tohoku Math. J. (2) 72(4): 595-619 (2020). DOI: 10.2748/tmj.20191030

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 étale cycle map, we will compare this filtration with a filtration on the étale 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. "A filtration on the higher Chow group of zero cycles on an abelian variety." Tohoku Math. J. (2) 72 (4) 595 - 619, 2020. https://doi.org/10.2748/tmj.20191030

Information

Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194189
Digital Object Identifier: 10.2748/tmj.20191030

Subjects:
Primary: 14C25
Secondary: 11G10, 14C35, 14G20

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 4 • 2020
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