Logo Reciprocity Archive
Register Reset password

Voevodsky's motives and Weil reciprocity

Bruno Kahn and Takao Yamazaki

We describe Somekawa's K-group associated to a finite collection of semi-abelian varieties (or more general sheaves) in terms of the tensor product in Voevodsky's category of motives. While Somekawa's definition is based on Weil reciprocity, Voevodsky's category is based on homotopy invariance. We apply this to explicit descriptions of certain algebraic cycles.

Reference : Duke Math. J. 162, no. 14 (2013), 2751-2796 10.1215/00127094-2381379

ArXiv link : https://arxiv.org/abs/1108.2764

Hal link : https://hal.archives-ouvertes.fr/hal-00614603v2

Pdf :
Last version : 16-07-2021