Displaying similar documents to “Bounds For Étale Capitulation Kernels II”

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 .

On the maximal unramified pro-2-extension over the cyclotomic ℤ 2 -extension of an imaginary quadratic field

Yasushi Mizusawa (2010)

Journal de Théorie des Nombres de Bordeaux

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For the cyclotomic ℤ 2 -extension k ∞ of an imaginary quadratic field k , we consider the Galois group G ( k ∞ ) of the maximal unramified pro- 2 -extension over k ∞ . In this paper, we give some families of k for which G ( k ∞ ) is a metabelian pro- 2 -group with the explicit presentation, and determine the case that G ( k ∞ ) becomes a nonabelian metacyclic pro- 2 -group. We also calculate Iwasawa theoretically the Galois groups of 2 -class field towers of certain cyclotomic 2 -extensions.

Fast computation of class fields given their norm group

Loïc Grenié (2008)

Journal de Théorie des Nombres de Bordeaux

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Let K be a number field containing, for some prime ℓ , the ℓ -th roots of unity. Let L be a Kummer extension of degree ℓ of K characterized by its modulus 𝔪 and its norm group. Let K 𝔪 be the compositum of degree ℓ extensions of K of conductor dividing 𝔪 . Using the vector-space structure of Gal ( K 𝔪 / K ) , we suggest a modification of the function of which brings the complexity of the computation of an equation of L over K from exponential to linear.

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

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The Steinitz class of a number field extension K / k is an ideal class in the ring of integers 𝒪 k of k , which, together with the degree [ K : k ] of the extension determines the 𝒪 k -module structure of 𝒪 K . We denote by R t ( k , G ) the set of classes which are Steinitz classes of a tamely ramified G -extension of k . We will say that those classes are realizable for the group G ; it is conjectured that the set of realizable classes is always a group. In this paper we will develop some of the ideas contained...

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...