English

A remark on the tensor product of SC-reciprocity sheaves

Algebraic Geometry 2019-11-15 v3

Abstract

We give a description of the tensor product of SC-reciprocity presheaves with transfers in terms of KK-group of geometric type, and we study a structure of the tensor product of Ga\mathbb{G}_a and Ga\mathbb{G}_a. We apply our description to give a description of Chow group of 0-cycles with modulus of products of curves. We also show that the tensor product of Ga\mathbb{G}_a and Gm\mathbb{G}_m is isomorphic to the sheaf Ω1\Omega^1 of K\"ahler differential forms as reciprocity sheaves over characteristic zero.

Keywords

Cite

@article{arxiv.1704.03638,
  title  = {A remark on the tensor product of SC-reciprocity sheaves},
  author = {Rin Sugiyama},
  journal= {arXiv preprint arXiv:1704.03638},
  year   = {2019}
}

Comments

The notion of tensor product in the category of SC-reciprocity sheaves was not correct. We don't know whether this category has a symmetric monoidal structure. But the results in this paper survive in much more suitable way. See arXiv:1911.05291