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arXiv · 1804.10153

Tensor products of affine and formal abelian groups

Tilman Bauer·Magnus Carlson
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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 Dieudonn\'e theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.

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Tilman Bauer, Magnus Carlson. 2018-04-26. Tensor products of affine and formal abelian groups. https://arxiv.org/abs/1804.10153

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