Tensor products of affine and formal abelian groups

Tilman Bauer; Magnus Carlson

paper

Tensor products of affine and formal abelian groups

arXiv:1804.10153

Abstract

In this paper we study tensor products of affine abelian group schemes over a perfect field $k .$ We first prove that the tensor product $G_{1} \otimes G_{2}$ of two affine abelian group schemes $G_{1}, G_{2}$ over a perfect field $k$ exists. We then describe the multiplicative and unipotent part of the group scheme $G_{1} \otimes G_{2}$ . The multiplicative part is described in terms of Galois modules over the absolute Galois group of $k .$ We describe the unipotent part of $G_{1} \otimes G_{2}$ explicitly, using Dieudonné theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.

arXiv comment46 pages, comments welcome