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arXiv · 2112.09525

Leopoldt-type theorems for non-abelian extensions of Q

Fabio Ferri
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Abstract

We prove new results concerning the additive Galois module structure of certain wildly ramified finite non-abelian extensions of Q. In particular, when K/Q is a Galois extension with Galois group G isomorphic to A4, S4 or A5, we give necessary and sufficient conditions for the ring of integers of K to be free over its associated order in the rational group algebra Q[G].

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Fabio Ferri. 2021-12-17. Leopoldt-type theorems for non-abelian extensions of Q. https://arxiv.org/abs/2112.09525

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