Wild primes of a self-equivalence of a number field

Alfred Czogała, and Beata Rothkegel. "Wild primes of a self-equivalence of a number field." Acta Arithmetica 166.4 (2014): 335-348. <http://eudml.org/doc/278931>.

@article{AlfredCzogała2014,
abstract = {Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of $_i$ is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at $_i$ for every nondyadic $_i ∈ \{₁,...,ₙ\}$, then ₁,...,ₙ is the wild set of some self-equivalence of the field K.},
author = {Alfred Czogała, Beata Rothkegel},
journal = {Acta Arithmetica},
keywords = {self-equivalence; wild prime; class field theory},
language = {eng},
number = {4},
pages = {335-348},
title = {Wild primes of a self-equivalence of a number field},
url = {http://eudml.org/doc/278931},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Alfred Czogała
AU - Beata Rothkegel
TI - Wild primes of a self-equivalence of a number field
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 4
SP - 335
EP - 348
AB - Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of $_i$ is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at $_i$ for every nondyadic $_i ∈ {₁,...,ₙ}$, then ₁,...,ₙ is the wild set of some self-equivalence of the field K.
LA - eng
KW - self-equivalence; wild prime; class field theory
UR - http://eudml.org/doc/278931
ER -