Bauer, Tilman; Carlson, Magnus

Tensor Products of Affine and Formal Abelian Groups

Doc. Math. 24, 2525-2582 (2019)
DOI: 10.25537/dm.2019v24.2525-2582
Communicated by Mike Hill

Summary

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.

Mathematics Subject Classification

14L17, 16W30, 14L05

Keywords/Phrases

Dieudonné theory, affine group schemes, tensor products, formal groups

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Affiliation

Bauer, Tilman
Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden
Carlson, Magnus
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

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