• Corpus ID: 115464182

On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields

@inproceedings{Onabe1976OnTI,
  title={On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields},
  author={Midori Onabe},
  year={1976},
  url={https://api.semanticscholar.org/CorpusID:115464182}
}
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17 Citations
Highly Influential Citations
4
Background Citations
8
Methods Citations
2
Results Citations
1

17 Citations

ANTS X Proceedings of the Tenth Algorithmic Number Theory Symposium msp Imaginary quadratic fields with isomorphic abelian Galois groups

Two-step nilpotent extensions are not anabelian

We prove the existence of two non-isomorphic number fields $K$ and $L$ such that the maximal two-step nilpotent quotients of their absolute Galois groups are isomorphic. In particular, one may take…

A program to test the p-rationality of any number field

Let K be a number field. We prove that its ray class group modulo p 2 (resp. 8) if p > 2 (resp. p = 2) characterizes its p-rationality. Then we give two short, very fast PARI Programs (§ § 3.1, 3.2)…

On p-rationality of number fields. Applications – PARI/GP programs

— LetK be a number field. We prove that its ray class group modulo p2 (resp. 8) if p > 2 (resp. p = 2) characterizes its p-rationality. Then we give two short and very fast PARI Programs (Sections…

The m-step Solvable Hom-Form of Birational Anabelian Geometry for Number Fields

In 1981, Uchida proved a conditional version of the Hom-form of the Grothendieck birational anabelian conjecture for number fields. In this paper we prove an m-step solvable conditional version of…

Practice of the Incomplete $p$-Ramification Over a Number Field -- History of Abelian $p$-Ramification

The theory of p-ramification in the maximal prop extension of a number field K, unramified outside p and $\infty$, is well known including numerical experiments with PARI/GP programs. The case of…

L-series and isomorphisms of number fields

Characterization of global fields by Dirichlet L-series

We prove that two global fields are isomorphic if and only if there is an isomorphism of groups of Dirichlet characters that preserves L-series.

Reconstructing global fields from dynamics in the abelianized Galois group

We study a dynamical system induced by the Artin reciprocity map for a global field. We translate the conjugacy of such dynamical systems into various arithmetical properties that are equivalent to…

Reconstructing global fields from Dirichlet L-series

We prove that two global fields are isomorphic if and only if there is an isomorphism of groups of Dirichlet characters that preserves L-series.