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

Alfred Czogała; Beata Rothkegel; Andrzej Sładek

doi:10.1515/amsil-2016-0008

.blurhash-client-img { display: none !important; }

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

Annales Mathematicae Silesianae

Volume 30 (2016): Issue 1 (September 2016)

By: Alfred Czogała, Beata Rothkegel and Andrzej Sładek

Open Access

|Sep 2016

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 C_K. 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.

References

[1] Cassels J.W., Fröhlich A., Algebraic Number Theory, Academic Press, London, 1967.
Search in Google Scholar Back to article
[2] Czogała A., Sładek A., Higher degree Hilbert symbol equivalence of number fields, Tatra Mountains Math. Publ. 11 (1997), 77–88.
Search in Google Scholar Back to article
[3] Czogała A., Sładek A., Higher degree Hilbert symbol equivalence of number fields II, J. Number Theory 72 (1998), 363–376.10.1006/jnth.1998.2266
Search in Google Scholar Back to article
[4] Czogała A., Higher degree tame Hilbert-symbol equivalence of number fields,. Abh. Math. Sem. Univ. Hamburg 69 (1999), 175–185.10.1007/BF02940871
Search in Google Scholar Back to article
[5] Czogała A., On reciprocity equivalence of quadratic number fields, Acta Arith. 58 (1991), 27–46.10.4064/aa-58-1-27-46
Search in Google Scholar Back to article
[6] Czogała A., Witt rings of Hasse domains of global fields, J. Algebra 244 (2001), 604–630.10.1006/jabr.2001.8918
Search in Google Scholar Back to article
[7] Czogała A., Rothkegel B., Wild primes of a self-equivalence of a number field, Acta Arith. 166 (2014), 27–46.10.4064/aa166-4-2
Search in Google Scholar Back to article
[8] Leep D.B., Wadsworth A.R., The Hasse norm theorem mod squares, J. Number Theory 42 (1991), 337–348.10.1016/0022-314X(92)90098-A
Search in Google Scholar Back to article
[9] Milnor J., Algebraic K-Theory and quadratic forms, Invent. Math. 9 (1970), 318–344.10.1007/BF01425486
Search in Google Scholar Back to article
[10] Neukirch J., Class Field Theory, Springer-Verlag, Berlin, 1986.10.1007/978-3-642-82465-4
Search in Google Scholar Back to article
[11] Perlis R., Szymiczek K., Conner P., Litherland R., Matching Witts with global fields, Contemp. Math. 155 (1994), 365–387.10.1090/conm/155/01393
Search in Google Scholar Back to article
[12] Rothkegel B., Czogała A., Singular elements and the Witt equivalence of rings of algebraic integers, Ramanujan J. 17 (2008), 185–217.10.1007/s11139-008-9119-z
Search in Google Scholar Back to article
[13] Somodi M., On the size of the wild set, Canad. J. Math. 55 (2005), 180–203.
Search in Google Scholar Back to article
[14] Somodi M., A characterization of the finite wild sets of rational self-equivalences, Acta Arith. 121 (2006), 327–334.10.4064/aa121-4-3
Search in Google Scholar Back to article
[15] Somodi M., Self-equivalences of the Gaussian field, Rocky Mountain J. Math. 38 (2008), 2077–2089.10.1216/RMJ-2008-38-6-2077
Search in Google Scholar Back to article
[16] Sładek A., Hilbert symbol equivalence and Milnor K-functor, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 183–190.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/amsil-2016-0008 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 17 - 38

Submitted on: Apr 5, 2016

Accepted on: Jun 1, 2016

Published on: Sep 23, 2016

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

higher degree Hilbert-symbol equivalence,

wild prime

Related subjects:

Mathematics,

General mathematics

© 2016 Alfred Czogała, Beata Rothkegel, Andrzej Sładek, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2016): Issue 1 (September 2016)