Geodesic
Tensor Products of Affine and Formal Abelian Groups
Documenta mathematica, Tome 24 (2019), pp. 2525-2582
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In this paper we study tensor products of affine abelian group schemes over a perfect field k. We first prove that the tensor product G1​⊗G2​ of two affine abelian group schemes G1​,G2​ over a perfect field k exists. We then describe the multiplicative and unipotent part of the group scheme G1​⊗G2​. The multiplicative part is described in terms of Galois modules over the absolute Galois group of k. We describe the unipotent part of G1​⊗G2​ explicitly, using Dieudonné theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.
DOI : 10.4171/dm/733
Classification : 14L05, 14L17
Mots-clés : affine group schemes, formal groups, Dieudonné theory, tensor products 
@article{10_4171_dm_733,
     author = {Tilman Bauer and Magnus Carlson},
     title = {Tensor {Products} of {Affine} and {Formal} {Abelian} {Groups}},
     journal = {Documenta mathematica},
     pages = {2525--2582},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/733},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/733/}
}
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Tilman Bauer; Magnus Carlson. Tensor Products of Affine and Formal Abelian Groups. Documenta mathematica, Tome 24 (2019), pp. 2525-2582. doi: 10.4171/dm/733

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