학술논문

Tensor products of affine and formal abelian groups
Document Type
Working Paper
Source
Subject
Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
14L17, 16W30, 14L05
Language
Abstract
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 Dieudonn\'e theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.
Comment: 46 pages, comments welcome