The $S$-relative P\'olya groups and $S$-Ostrowski quotients of number fields

Ehsan Shahoseini; Abbas Maarefparvar

The $S$-relative P\'olya groups and $S$-Ostrowski quotients of number fields

Number Theory 2023-12-18 v1

Authors: Ehsan Shahoseini , Abbas Maarefparvar

Abstract

Let $K/F$ be a finite extension of number fields and $S$ be a finite set of primes of $F$ , including all the archimedean ones. In this paper, using some results of Gonz\'alez-Avil\'es \cite{Aviles}, we generalize the notions of the relative P\'olya group $\Po(K/F)$ \cite{ChabertI,MR2} and the Ostrowski quotient $\Ost(K/F)$ \cite{SRM} to their $S$ -versions. Using this approach, we obtain generalizations of some well-known results on the $S$ -capitulation map, including an $S$ -version of Hilbert's theorem 94.

Keywords

number fields S-relative Pólya groups S-Ostrowski quotients S-capitulation map Hilbert's theorem 94 finite extension

Cite

@article{arxiv.2312.09362,
  title  = {The $S$-relative P\'olya groups and $S$-Ostrowski quotients of number fields},
  author = {Ehsan Shahoseini and Abbas Maarefparvar},
  journal= {arXiv preprint arXiv:2312.09362},
  year   = {2023}
}

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9 pages

The $S$-relative P\'olya groups and $S$-Ostrowski quotients of number fields

Abstract

Keywords

Cite

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