<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Let ℓ > 2 be a prime number. Let <italic>K</italic> be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group <italic>C<sub>K</sub></italic>. The main theorem of the paper gives a sufficient condition for a finite set of primes of <italic>K</italic> to be the wild set of some Hilbert self-equivalence of <italic>K</italic> of degree ℓ.</p></abstract>

Let ℓ > 2 be a prime number. Let K be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group CK. The main theorem of the paper gives a sufficient condition for a finite set of primes of K to be the wild set of some Hilbert self-equivalence of K of degree ℓ.

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

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

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Wild Primes of a Higher Degree Self-Equivalence of a Number Field"}

Let ℓ > 2 be a prime number. Let K be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group CK. The main...

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

Published Online: Sep 23, 2016

Page range: 17 - 38

Received: Apr 05, 2016

Accepted: Jun 01, 2016

DOI: https://doi.org/10.1515/amsil-2016-0008

Keywords
higher degree Hilbert-symbol equivalence, wild prime

© 2016 Alfred Czogała et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

Published Online: Sep 23, 2016

Page range: 17 - 38

Received: Apr 05, 2016

Accepted: Jun 01, 2016

DOI: https://doi.org/10.1515/amsil-2016-0008

Keywordshigher degree Hilbert-symbol equivalence, wild prime

© 2016 Alfred Czogała et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
higher degree Hilbert-symbol equivalence, wild prime