Geodesic
Leopoldt-type theorems for non-abelian extensions of $\mathbb{Q}$
Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 308-337

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DOI

We prove new results concerning the additive Galois module structure of wildly ramified non-abelian extensions $K/\mathbb{Q}$ with Galois group isomorphic to $A_4$, $S_4$, $A_5$, and dihedral groups of order $2p^n$ for certain prime powers $p^n$. In particular, when $K/\mathbb{Q}$ is a Galois extension with Galois group $G$ isomorphic to $A_4$, $S_4$ or $A_5$, we give necessary and sufficient conditions for the ring of integers $\mathcal{O}_{K}$ to be free over its associated order in the rational group algebra $\mathbb{Q}[G]$.
DOI : 10.1017/S0017089523000460
Mots-clés : algebraic number theory, Galois module structure, wild ramification, associated orders, normal integral bases 
Ferri, Fabio. Leopoldt-type theorems for non-abelian extensions of $\mathbb{Q}$. Glasgow mathematical journal, Tome 66 (2024) no. 2, pp. 308-337. doi: 10.1017/S0017089523000460
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     title = {Leopoldt-type theorems for non-abelian extensions of $\mathbb{Q}$},
     journal = {Glasgow mathematical journal},
     pages = {308--337},
     year = {2024},
     volume = {66},
     number = {2},
     doi = {10.1017/S0017089523000460},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000460/}
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