Voevodsky's motives and Weil reciprocity

Abstract

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.

arXiv commentRevised version; the title and introduction were changed. arXiv admin note: substantial text overlap with arXiv:1009.4554

References in corpus (2)

• Cancellation theorem
• Duality of Albanese and Picard 1-motives

Cited by in corpus (6)

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• Motives with modulus, III: The categories of motives
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• An additive variant of the differential symbol maps
• Steinberg symbols and reciprocity sheaves
• The local symbol complex of a Reciprocity Functor