Leopoldt-type theorems for non-abelian extensions of Q

2021/12/17 by Ferri, Fabio
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.09525

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].

Related

• Relative Galois module structure of rings of integers of absolutely Abelian number fields
• Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold
• Galois extensions ramified only at one prime
• On the restricted Hilbert-Speiser and Leopoldt properties
• Unramified extensions over low degree number fields