Wild primes of a self-equivalence of a number field

• Autorzy: Alfred Czogała , Beata Rothkegel
• Języki publikacji: EN

Abstrakty

EN

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 𝔡 and the class of 𝔡 is a square in the ideal class group of K. We prove that if 𝔭₁,...,𝔭ₙ are finite primes of K such that
∙ the class of $𝔭_i$ is a square in the ideal class group of K for every i ∈ {1,...,n},
∙ -1 is a local square at $𝔭_i$ for every nondyadic $𝔭_i ∈ {𝔭₁,...,𝔭ₙ}$,
then {𝔭₁,...,𝔭ₙ} is the wild set of some self-equivalence of the field K.

Kategorie tematyczne

• 11E12: Quadratic forms over global rings and fields
• 11E81: Algebraic theory of quadratic forms; Witt groups and rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 4
• Strony: 335-348

Daty

wydano

2014

Twórcy

autor

Alfred Czogała

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

autor

Beata Rothkegel

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/aa166-4-2