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 is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at for every nondyadic , then ₁,...,ₙ is the wild set of some self-equivalence of the field K.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-2,
author = {Alfred Czoga\l a and Beata Rothkegel},
title = {Wild primes of a self-equivalence of a number field},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {335-348},
zbl = {1319.11077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-2}
}
Alfred Czogała; Beata Rothkegel. Wild primes of a self-equivalence of a number field. Acta Arithmetica, Tome 166 (2014) pp. 335-348. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-2/