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

Daniel Gil-Muñoz

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arXiv · 2410.10383

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

Daniel Gil-Muñoz

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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 $L/K$.

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Daniel Gil-Muñoz. 2024-10-14. Hopf-Galois module structure of degree p extensions of p-adic fields. https://arxiv.org/abs/2410.10383

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