Geodesic
Tensor Products of Affine and Formal Abelian Groups
Documenta mathematica, Tome 24 (2019), pp. 2525-2582.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14L17, 16W30, 14L05
Keywords: Dieudonné theory, affine group schemes, tensor products, formal groups 
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     author = {Bauer, Tilman and Carlson, Magnus},
     title = {Tensor {Products} of {Affine} and {Formal} {Abelian} {Groups}},
     journal = {Documenta mathematica},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a2/}
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Bauer, Tilman; Carlson, Magnus. Tensor Products of Affine and Formal Abelian Groups. Documenta mathematica, Tome 24 (2019), pp. 2525-2582. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a2/