Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 595-619

Title A FILTRATION ON THE HIGHER CHOW GROUP OF ZERO CYCLES ON AN ABELIAN VARIETY

Author Buntaro Kakinoki

(Received January 16, 2019, revised October 15, 2019)
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.

Mathematics Subject Classification. Primary 14C25; Secondary 14C35, 14G20, 11G10.
Key words and phrases. Gazaki type filtration, higher Chow groups of zero cycles, Somekakawa type $K$-group, étale cycle map, reciprocity map.

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