Displaying similar documents to “Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2 ”

On Galois structure of the integers in cyclic extensions of local number fields

G. Griffith Elder (2002)

Journal de théorie des nombres de Bordeaux

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Let p be a rational prime, K be a finite extension of the field of p -adic numbers, and let L / K be a totally ramified cyclic extension of degree p n . Restrict the first ramification number of L / K to about half of its possible values, b 1 > 1 / 2 · p e 0 / ( p - 1 ) where e 0 denotes the absolute ramification index of K . Under this loose condition, we explicitly determine the ℤ p [ G ] -module structure of the ring of integers of L , where ℤ p denotes the p -adic integers and G denotes the Galois group Gal ( L / K ) . In the process of determining...

Galois module structure of generalized jacobians.

G. D. Villa-Salvador, M. Rzedowski-Calderón (1997)

Revista Matemática de la Universidad Complutense de Madrid

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For a prime number l and for a finite Galois l-extension of function fields L / K over an algebraically closed field of characteristic p <> l, it is obtained the Galois module structure of the generalized Jacobian associated to L, l and the ramified prime divisors. In the cyclic case an implicit integral representation of the Jacobian is obtained and this representation is compared with the explicit representation.

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...

Lubin-Tate formal groups and module structure over Hopf orders

Werner Bley, Robert Boltje (1999)

Journal de théorie des nombres de Bordeaux

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Over the last years Hopf orders have played an important role in the study of integral module structures arising in arithmetic geometry in various situations. We axiomatize these situations and discuss the properties of the (integral) Hopf algebra structures which are of interest in this general setting. In particular, we emphasize the role of resolvents for explicit computations. As an illustration we apply our results to determine the Hopf module structure of the ring of integers in...

Some counter-examples in the theory of the Galois module structure of wild extensions

Stephen M. J. Wilson (1980)

Annales de l'institut Fourier

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Considering the ring of integers in a number field as a Z Γ -module (where Γ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.

Galois module structure of the rings of integers in wildly ramified extensions

Stephen M. J. Wilson (1989)

Annales de l'institut Fourier

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The main results of this paper may be loosely stated as follows. Theorem.— Let N and N ' be sums of Galois algebras with group Γ over algebraic number fields. Suppose that N and N ' have the same dimension ℚ and that they are identical at their wildly ramified primes. Then (writing 𝒪 N for the maximal order in N ) 𝒪 N ⊕ 𝒪 N ⊕ ℤ Γ ≅ ℤ Γ ⊕ 𝒪 N ' ⊕ 𝒪 N ' ⊕ ℤ Γ .