Reciprocity sheaves, II

We exhibit an intimate relationship between "reciprocity sheaves" from arXiv:1402.4201 [math.AG] and "modulus sheaves with transfers" from arXiv:1908.02975 [math.AG] and arXiv:1910.14534 [math.AG].Comment: A mistake in arXiv:1511.07124 [math.AG] pointed out by Ayoub has been repaired, so the previous paper is restored with a changed titl

Voevodsky's motives and Weil reciprocity

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.Comment: Revised version; the title and introduction were changed. arXiv admin note: substantial text overlap with arXiv:1009.455