Abstract
Let p be an odd prime number. We construct explicit uniformizers for the totally ramified extension \({\mathbb {Q}}_p(\zeta _{p^2},\root p \of {p})\) of the field of p-adic numbers \({\mathbb {Q}}_p\), where \(\zeta _{p^2}\) is a primitive \(p^2\)-th root of unity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kim, B.D.: Signed-Selmer groups over the \(\mathbb{Z}_p^2\)-extension of an imaginary quadratic field. Can. J. Math. 66(4), 826–843 (2014)
Kim, B.D.: Ranks of the rational points of abelian varieties over ramified fields, and Iwasawa theory for primes with non-ordinary reduction. J. Number Theory 183, 352–387 (2018)
Kobayashi, S.: Iwasawa theory for elliptic curves at supersingular primes. Invent. Math. 152(1), 1–36 (2003)
StackExchange. https://math.stackexchange.com/questions/954731/ (2014). Accessed 10 Aug 2018
Viviani, F.: Ramification groups and Artin conductors of radical extensions of \(\mathbb{Q}\). J. Théor. Nr. Bordx. 16(3), 779–816 (2004)
Acknowledgements
This work was carried out during two NSERC summer research internships undertaken by the first named author at Université Laval in 2018 and 2019. The second named author’s research is supported by the NSERC Discovery Grants Program 05710. We would like to thank Hugo Chapdelaine, Daniel Delbourgo, Cédric Dion, Byoung Du Kim and Antoine Poulin for helpful and interesting discussions during the preparation of this article. Finally, we thank the anonymous referee for valuable comments and suggestions on an earlier version of the article.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Jens Funke.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bellemare, H., Lei, A. Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers. Abh. Math. Semin. Univ. Hambg. 90, 73–83 (2020). https://doi.org/10.1007/s12188-020-00215-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12188-020-00215-x