On the fourth power level of $\mathfrak{p}$-adic completions of biquadratic number fields
Abstract
Let $K$ be a number field and $\mathfrak{p} \mid (2)$ be a prime ideal. We compute the fourth level of the $\mathfrak{p}$-adic completions of $K$ when the ramification index is $4$ and the inertial degree is trivial for the ideal $\mathfrak{p}$. This enables the computation of the fourth level of the $\mathfrak{p}$-adic completion of any quartic number field for any prime $\mathfrak{p} \mid (2)$. Here, we apply this result to biquadratic number fields and obtain lower bounds for the fourth level of such number fields.
Fields of Study & Subjects
advanced mathematical theories
Algebraic Geometry and Number Theory
Meromorphic and Entire Functions
Publication details
- Journal / source
- Functiones et Approximatio Commentarii Mathematici
- Publisher
- Adam Mickiewicz University (Euclid)
- Volume
- -1
- Issue
- -1
- Pages
- 1–27
- Publication date
- 1 January 2026
- Language
- EN