A remark on the tensor product of SC-reciprocity sheaves

Abstract

We give a description of the tensor product of SC-reciprocity presheaves with transfers in terms of $K$-group of geometric type, and we study a structure of the tensor product of ${\mathbb{G}}_a$ and ${\mathbb{G}}_a$. 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 ${\mathbb{G}}_a$ and ${\mathbb{G}}_m$ is isomorphic to the sheaf ${\Omega }^1$ of Kähler differential forms as reciprocity sheaves over characteristic zero.

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

References in corpus (4)

• Zero cycles with modulus and zero cycles on singular varieties
• Reciprocity sheaves
• Motives with modulus
• Purity of reciprocity sheaves