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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Abstract

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.

Cite this article

Tilman Bauer, Magnus Carlson, Tensor Products of Affine and Formal Abelian Groups. Doc. Math. 24 (2019), pp. 2525–2582

DOI 10.4171/DM/733