Galois module structure of the square root of the inverse different in even degree tame extensions of number fields

Caputo, Luca; Vinatier, Stéphane

doi:10.1016/j.jalgebra.2016.06.035

Cited by 7 publications

(17 citation statements)

References 23 publications

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“…Although we do not pursue it here, we believe it likely that the same local approach would also shed light on several of the explicit questions that were recently raised by Caputo and Vinatier in the introduction to [16].…”

Section: Introductionmentioning

confidence: 99%

On refined metric and hermitian structures in arithmetic, I : Galois–Gauss sums and weak ramification

Bley

Burns

Hahn³

2020

Ann. K-Th.

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Section: Introductionmentioning

confidence: 99%

On refined metric and hermitian structures in arithmetic, I : Galois–Gauss sums and weak ramification

Bley

Burns

Hahn³

2020

Ann. K-Th.

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“…Conjecture 1.4 includes Vinatier's Conjecture 1.2 as a special case, and was the motivation for the work described in [5]. It also explains almost all previously obtained results on the ZG-structure of A(π).…”

Section: Introductionmentioning

confidence: 58%

“…The first detailed study of the Galois structure of A(π) when |G| is even is due to the second-named author and Vinatier [5]. By studying the Galois structure of certain torsion modules first considered by S. Chase [6], they proved the following result,and thereby were able to exhibit the first examples for which (A(π)) = 0 in Cl(ZG) (see [5,Theorem 2]).…”

Section: Introductionmentioning

confidence: 99%

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On the square root of the inverse different

Agboola¹,

Caputo²

2018

Preprint

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Let F π /F be a finite, Galois-algebra extension of number fields with group G. Suppose that F π /F is weakly ramified, and that the square root A(π) of the inverse different D(π) −1 is defined. (This latter condition holds if, for example, |G| is odd.) B. Erez has conjectured that the class (A(π)) of A(π) in the locally free class group Cl(ZG) of ZG is equal to Chinburg's invariant Ω(F π /F, 2). We show that this equality holds whenever A(π) is defined and F π /F is tame. This extends a result of the second-named author and S. Vinatier.

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“…Using tools from [4], L. Caputo and S. Vinatier showed in [3] that Question 1.1 also admits an affirmative answer as long as L/K is locally abelian.…”

Section: Introductionmentioning

confidence: 99%

On the self-duality of rings of integers in tame and abelian extensions

Tsang

2017

Preprint

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Let L/K be a tame and Galois extension of number fields with group G. It is well-known that any ambiguous ideal in L is locally free over O K G (of rank one), and so it defines a class in the locally free class group of O K G, where O K denotes the ring of integers of K. In this paper, we shall study the relationship among the classes arising from the ring of integers O L of L, the inverse different D −1 L/K of L/K, and the square root of the inverse different A L/K of L/K (if it exists), in the case that G is abelian. They are naturally related because A

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Galois module structure of the square root of the inverse different in even degree tame extensions of number fields

Cited by 7 publications

References 23 publications

On refined metric and hermitian structures in arithmetic, I : Galois–Gauss sums and weak ramification

On refined metric and hermitian structures in arithmetic, I : Galois–Gauss sums and weak ramification

On the square root of the inverse different

On the self-duality of rings of integers in tame and abelian extensions

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