Daniel Gil-Muñoz

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20242026

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math.NT2026

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

Daniel Gil-MuÃ±oz

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 $O_{L}$ t…

math.NT2025

Hopf-Galois module structure of monogenic orders in cubic number fields

Daniel Gil-MuÃ±oz

For a cubic number field $L$ , we consider the $Z$ -order in $L$ of the form $Z [I^\pm]$ , where $I^\pm$ is a root of a polynomial of the form $x^{3} - a x + b$ and $a,b\in\mathbb…

math.NT2025

Additive structure of non-monogenic simplest cubic fields

We consider Shanks' simplest cubic fields $K$ for which the index $[O_{K} : Z [I ¨ ]]$ of a root $I ¨ $ of the defining parametric polynomial is $3$ . For them, we study t…

math.NT2024

A generalization of Kummer theory to Hopf-Galois extensions

Daniel Gil-MuÃ±oz

We introduce a condition for Hopf-Galois extensions that generalizes the notion of Kummer Galois extension. Namely, an $H$ -Galois extension $L / K$ is $H$ -Kummer if $L$ can be genera…