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arXiv · 2111.00442

Ostrowski quotients for finite extensions of number fields

Ehsan Shahoseini·Ali Rajaei·Abbas Maarefparvar
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Abstract

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 $\Po(L/K)$, in the works of Brumer-Rosen and Zantema, we find short proofs for some classical results in the literatur. 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 $\Po(L/\mathbb{Q})$ to $\Ost(L/K)$.

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Ehsan Shahoseini, Ali Rajaei, Abbas Maarefparvar. 2022-06-20. Ostrowski quotients for finite extensions of number fields. https://doi.org/10.2140/pjm.2022.321.415

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