In this paper we study tensor products of affine abelian group schemes over a perfect field . We first prove that the tensor product of two affine abelian group schemes over a perfect field exists. We then describe the multiplicative and unipotent part of the group scheme . The multiplicative part is described in terms of Galois modules over the absolute Galois group of . We describe the unipotent part of explicitly, using Dieudonné theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.
Cite this article
Tilman Bauer, Magnus Carlson, Tensor Products of Affine and Formal Abelian Groups. Doc. Math. 24 (2019), pp. 2525–2582DOI 10.4171/DM/733