Displaying similar documents to “A classification of the extensions of degree p 2 over ℚ p whose normal closure is a p -extension”

Conjugacy classes of series in positive characteristic and Witt vectors.

Sandrine Jean (2009)

Journal de Théorie des Nombres de Bordeaux

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Let k be the algebraic closure of 𝔽 p and K be the local field of formal power series with coefficients in k . The aim of this paper is the description of the set 𝒴 n of conjugacy classes of series of order p n for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic p which are invertible and of finite order p n for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series...

Constructing class fields over local fields

Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

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Let K be a 𝔭 -adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L / K of degree p to the exponents of generators of the norm group N L / K ( L * ) . This is applied in an algorithm for the construction of class fields of degree p m , which yields an algorithm for the computation of class fields in general.

Absolute norms of p -primary units

Supriya Pisolkar (2009)

Journal de Théorie des Nombres de Bordeaux

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We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2 -primary units. We also prove a similar statement about the absolute norms of p -primary units, for all primes p .

Wintenberger’s functor for abelian extensions

Kevin Keating (2009)

Journal de Théorie des Nombres de Bordeaux

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Let k be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian p -adic Lie extensions E / F , where F is a local field with residue field k , and a category whose objects are pairs ( K , A ) , where K ≅ k ( ( T ) ) and A is an abelian p -adic Lie subgroup of Aut k ( K ) . In this paper we extend this equivalence to allow Gal ( E / F ) and A to be arbitrary abelian pro- p groups.

Note on the Galois module structure of quadratic extensions

Günter Lettl (1994)

Colloquium Mathematicae

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In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, ℚ ( p ) . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of ℚ ( n ) / ℚ ( n ) + .