On the Galois module structure of extensions of local fields

Thomas, Lara

doi:10.5802/pmb.a-131

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The Case When the Associated Order Is Maximal1

Working With the 5-part1

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2014

2022

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Cited by 5 publications

(2 citation statements)

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“…If G is abelian, a necessary condition for the associated order to be maximal is that G is cyclic. For other considerations in the abelian case, see the survey of Thomas [28].…”

Section: The Case When the Associated Order Is Maximalmentioning

confidence: 99%

How far is an extension of $p$-adic fields from having a normal integral basis?

Corso¹,

Ferri²,

Lombardo³

2020

Preprint

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“…If G is abelian, a necessary condition for the associated order to be maximal is that G is cyclic. For other considerations in the abelian case, see the survey of Thomas [28].…”

Section: The Case When the Associated Order Is Maximalmentioning

confidence: 99%

How far is an extension of $p$-adic fields from having a normal integral basis?

Corso¹,

Ferri²,

Lombardo³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, the classical Galois structure F [λ(J)] is its unique Hopf Galois structure. The problem of the Galois module structure of the integers rings of such an extension was completely solved by F. Bertrandias, J.P. Bertrandias and M.J. Ferton (see [3] and [4] for the proof and [16,Theorem 3.4] for the statement):…”

Section: Working With the 5-partmentioning

confidence: 99%

Hopf Galois module structure of dihedral degree $2p$ extensions of $\mathbb{Q}_p$

Gil-Muñoz,

Rio

2020

Preprint

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Let p be an odd prime. For field extensions L/Q p with Galois group isomorphic to the dihedral group D 2p of order 2p, we consider the problem of computing a basis of the associated order in each Hopf Galois structure and the module structure of the ring of integers O L . We provide a complete solution for Hopf Galois structures of dihedral type and present a practical method for the cyclic type. We give a complete answer for p = 3 and p = 5 and we see that within this family of dihedral extensions we do not have a uniform behavior with respect to the ring of integers being free over the associated Hopf order.

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Artin–Schreier extensions and generalized associated orders

Huynh

2014

Journal of Number Theory

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On the Galois module structure of extensions of local fields

Abstract: Let K be a non archimedean local field of characteristic zero. F/K being a cyclic extension of degree p n , we determine the Z p [G]-module F × up to isomorphism.

Cited by 5 publications

References 99 publications

How far is an extension of $p$-adic fields from having a normal integral basis?

How far is an extension of $p$-adic fields from having a normal integral basis?

Hopf Galois module structure of dihedral degree $2p$ extensions of $\mathbb{Q}_p$

Artin–Schreier extensions and generalized associated orders

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