Abelian extensions generated by division points
type: Item
instance of: scholarly article
title: Abelian extensions generated by division points
zbMATH Open document ID: 0648.12018
DOI: 10.1016/0022-314X(88)90091-1
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: The authors discuss various number-theoretic applications of the following assertion [compare with the lemma of Sah in the book by \textit{S. Lang}, ``Elliptic curves: Diophantine analysis'' (1978; Zbl 0388.10001)]: Let \(R\) be a commutative ring with identity and \(G\) be a profinite group acting continuously on a discrete \(R\)-module \(A\). Let \(g\) be an element of the center of \(G\) and assume that \(g\) acts on \(A\) as multiplication by \(r\) for some \(r\) from \(R\). Then \(r-1\) kills all the cohomology groups \(H^i(G,A)\).
Mathematics Subject Classification ID: 12G05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 4057641
zbMATH Keywords: Galois cohomology
zbMATH Keywords: division points
author: David S. Dummit
author: Hershy Kisilevsky
MaRDI profile type: Publication
cites work: On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
cites work: Rational points of Abelian varieties with values in towers of number fields
cites work: Abelian binomials, power residues and exponential congruences
full work available at URL: 0022-314x(88)90091-1
OpenAlex ID: W2050498387
description: scientific article; zbMATH DE number 4057641