Abelian extensions generated by division points
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 \(H^i(G,A)\).
scientific article; zbMATH DE number 4057641