Exterior powers of \(\pi\)-divisible modules over fields
type: Item
instance of: scholarly article
title: Exterior powers of \(\pi\)-divisible modules over fields
zbMATH Open document ID: 1347.11081
author: S. Mohammad Hadi Hedayatzadeh
published in: Journal of Number Theory
publication date: 2014-06-25T00:00:00Z
review text: In many categories the existence of a natural tensor product, or exterior powers, is an innocent matter and would usually not deserve much attention. It is, however, an important question, for we would like to factor, say, an alternating pairing of objects over the second exterior power. For example, for Galois representations this should be innocent and a pairing on abelian varieties would induce such a pairing. However, as one moves to more geometric ``sources'' of Galois representations, the existence question becomes less and less clear. E.g., on the level of group schemes, it already requires a proof that such an exterior power is still representable as a group scheme itself. In the present paper, the author considers this question in the category of \(\pi\)-divisible modules (e.g., \(p\)-divisible modules à la Barsotti-Tate). Here, the existence of exterior powers is a rather delicate matter. They may, or may not exist, and the paper (as well as its sequel) give a clear and careful analysis of this problem, as well as a fundamental existence result.
reviewed by: Oliver Bräunling
Mathematics Subject Classification ID: 11S31
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 14G40
zbMATH DE Number: 6308441
zbMATH Keywords: \(p\)-divisible group
zbMATH Keywords: Barsotti-Tate group
zbMATH Keywords: Dieudonné theory
zbMATH Keywords: exterior power
zbMATH Keywords: display
MaRDI profile type: Publication
full work available at URL: j.jnt.2013.10.023
OpenAlex ID: W2062601063
cites work: \(t\)-motives
cites work: Q5602064
cites work: Q4156867
cites work: Moduli of \(p\)-divisible groups
cites work: The Heights of Formal A-Modules
cites work: Q3884236
DOI: 10.1016/J.JNT.2013.10.023
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description: scientific article; zbMATH DE number 6308441