Hopf-Galois module structure of degree p extensions of p-adic fields

Daniel Gil-Muñoz

Hopf-Galois module structure of degree p extensions of p-adic fields

Number Theory 2026-05-06 v2

Authors: Daniel Gil-Muñoz

Abstract

Let $p$ be an odd prime number. For a degree $p$ extension of $p$ -adic fields $L/K$ , we give a complete characterization of the condition for the ring of integers $\mathcal{O}_L$ to be free as a module over its associated order in the unique Hopf-Galois structure on $L/K$ .

Keywords

Hopf-Galois theory p-adic fields ring of integers module structure Galois extensions

Cite

@article{arxiv.2410.10383,
  title  = {Hopf-Galois module structure of degree p extensions of p-adic fields},
  author = {Daniel Gil-Muñoz},
  journal= {arXiv preprint arXiv:2410.10383},
  year   = {2026}
}

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