Tensor Products of Affine and Formal Abelian Groups

  • Tilman Bauer

    Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden
  • Magnus Carlson

    Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
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In this paper we study tensor products of affine abelian group schemes over a perfect field kk. We first prove that the tensor product G1G2G_1 \otimes G_2 of two affine abelian group schemes G1,G2G_1,G_2 over a perfect field kk exists. We then describe the multiplicative and unipotent part of the group scheme G1G2G_1 \otimes G_2. The multiplicative part is described in terms of Galois modules over the absolute Galois group of kk. We describe the unipotent part of G1G2G_1 \otimes G_2 explicitly, using Dieudonné 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, Tensor Products of Affine and Formal Abelian Groups. Doc. Math. 24 (2019), pp. 2525–2582

DOI 10.4171/DM/733