How far is an extension of $p$-adic fields from having a normal integral basis?

Ilaria Del Corso; Fabio Ferri; Davide Lombardo

How far is an extension of $p$-adic fields from having a normal integral basis?

Number Theory 2020-10-23 v2

Authors: Ilaria Del Corso , Fabio Ferri , Davide Lombardo

Abstract

Let $L/K$ be a finite Galois extension of $p$ -adic fields with group $G$ . It is well-known that $\mathcal{O}_L$ contains a free $\mathcal{O}_K[G]$ -submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree $p$ of $p$ -adic fields.

Keywords

galois theory field theory p-adic analysis

Cite

@article{arxiv.2005.07932,
  title  = {How far is an extension of $p$-adic fields from having a normal integral basis?},
  author = {Ilaria Del Corso and Fabio Ferri and Davide Lombardo},
  journal= {arXiv preprint arXiv:2005.07932},
  year   = {2020}
}

Comments

31 pages. v2: minor typos corrected (a factor 1/2 was missing in the statement of Proposition 3.5), results unchanged

How far is an extension of $p$-adic fields from having a normal integral basis?

Abstract

Keywords

Cite

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