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Corpus ID: 240354074

Ostrowski quotients for finite extensions of number fields

@inproceedings{Shahoseini2021OstrowskiQF,
title={Ostrowski quotients for finite extensions of number fields},
author={Ehsan Shahoseini and Ali Rajaei and Abbas Maarefparvar},
year={2021}
}

. For L/K a ﬁnite Galois extension of number ﬁelds, the relative P´olya 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/ Q ) to Ost… Expand

We find an exact sequence in term of Tate-Shafarevich groups (assuming being finite) X(E/K) and X(E/L) of elliptic curve E over a finite Galois extension L/K of number fields. This is the analogue of… Expand

Abstract Let L be a finite extension of a number field K with ring of integers and respectively. One can consider as a projective module over . The highest exterior power of as an module gives an… Expand

Then e(a, b) (which is obviously a unit of K) belongs to the ground field: 8(a, b) e k . According to Deuring, he proved this theorem for the case of an imaginary quadratic ground field k using… Expand

The structure of the relative genus field is used to study the class group of relative i-extensions. Application to class field towers of cyclic i-extensions of the rationals are given. Given a… Expand

In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk , the class number of K. The… Expand

A number field is called a Pólya field if the module of integer valued polynomials over that field is generated by (fi)i=0∞ over the ring of integers, with deg(fi)=i, i=0, 1, 2,... In this paper… Expand