Ostrowski quotients for finite extensions of number fields

For $L ∕ K$ , a finite Galois extension of number fields, the relative Pólya group $Po (L ∕ K)$ coincides with the group of strongly ambiguous ideal classes in $L ∕ K$ . In this paper, using a well-known exact sequence related to $Po (L ∕ K)$ from the works of Brumer and Rosen (1963) and Zantema (1982), we find short proofs for some classical results in the literature. Then we define the Ostrowski quotient $Ost (L ∕ K)$ as the cokernel of the capitulation map into $Po (L ∕ K)$ and generalize some known results for $Po (L ∕ ℚ)$ to $Ost (L ∕ K)$ .

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Keywords

Pólya group, relative Pólya group, Ostrowski quotient, Galois cohomology, capitulation problem

Mathematical Subject Classification

Primary: 11R29, 11R37, 11R34, 11R21

Milestones

Received: 17 January 2022

Revised: 22 June 2022

Accepted: 26 November 2022

Published: 21 March 2023

Authors

Ehsan Shahoseini
Department of Mathematics Tarbiat Modares University Tehran Iran

Ali Rajaei
Department of Mathematics Tarbiat Modares University Tehran Iran

Abbas Maarefparvar
School of Mathematics Institute for Research in Fundamental Sciences (IPM) Tehran Iran

Vol. 321, No. 2, 2022

Ehsan Shahoseini, Ali Rajaei and Abbas Maarefparvar

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors