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Abstract
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For
,
a finite Galois extension of number fields, the relative Pólya group
coincides with the group of strongly ambiguous ideal classes
in .
In this paper, using a well-known exact sequence related to
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
as the cokernel of the capitulation map into
and generalize some
known results for
to
.
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Keywords
Pólya group, relative Pólya group, Ostrowski quotient,
Galois cohomology, capitulation problem
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Mathematical Subject Classification
Primary: 11R29, 11R37, 11R34, 11R21
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Milestones
Received: 17 January 2022
Revised: 22 June 2022
Accepted: 26 November 2022
Published: 21 March 2023
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© 2022 MSP (Mathematical Sciences
Publishers). |
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