Displaying similar documents to “The cyclic subfield integer index”

On the Galois structure of the square root of the codifferent

D. Burns (1991)

Journal de théorie des nombres de Bordeaux

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Let L be a finite abelian extension of ℚ , with 𝒪 L the ring of algebraic integers of L . We investigate the Galois structure of the unique fractional 𝒪 L -ideal which (if it exists) is unimodular with respect to the trace form of L / ℚ .

Factorisability and wildly ramified Galois extensions

David J. Burns (1991)

Annales de l'institut Fourier

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Let L / K be an abelian extension of p -adic fields, and let 𝒪 denote the valuation ring of K . We study ideals of the valuation ring of L as integral representations of the Galois group Gal ( L / K ) . Assuming K is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an 𝒪 -order in the group algebra K [ Gal ( l / K ) ] . We obtain several general and also explicit new results.

Relative Galois module structure of integers of abelian fields

Nigel P. Byott, Günter Lettl (1996)

Journal de théorie des nombres de Bordeaux

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Let L / K be an extension of algebraic number fields, where L is abelian over ℚ . In this paper we give an explicit description of the associated order 𝒜 L / K of this extension when K is a cyclotomic field, and prove that o L , the ring of integers of L , is then isomorphic to 𝒜 L / K . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that 𝒜 L / K is the maximal order if L / K is a cyclic and totally wildly ramified extension which is linearly disjoint to ℚ ( m ' ) / K , where m ' is the conductor...

Galois module structure of rings of integers

Martin J. Taylor (1980)

Annales de l'institut Fourier

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Let E / F be a Galois extension of number fields with Γ = Gal ( E / F ) and with property that the divisors of ( E : F ) are non-ramified in E / Q . We denote the ring of integers of E by 𝒪 E and we study 𝒪 E as a Z Γ -module. In particular we show that the fourth power of the (locally free) class of 𝒪 E is the trivial class. To obtain this result we use Fröhlich’s description of class groups of modules and his representative for the class of ℰ E , together with new determinantal congruences for cyclic group rings and corresponding...