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Displaying 301 – 320 of 973

Galois extensions of height-one commuting dynamical systems

Ghassan Sarkis, Joel Specter (2013)

Journal de Théorie des Nombres de Bordeaux

We consider a dynamical system consisting of a pair of commuting power series under composition, one noninvertible and another nontorsion invertible, of height one with coefficients in the $p$ -adic integers. Assuming that each point of the dynamical system generates a Galois extension over the base field, we show that these extensions are in fact abelian, and, using results from the theory of the field of norms, we also show that the dynamical system must include a torsion series. From an earlier...

Galois ...-factors modulo roots of unity.

Guy Henniart (1984)

Inventiones mathematicae

Galois generators and the subspace theorem.

G.R. Everest (1986/1987)

Manuscripta mathematica

Galois module structure of abelian extensions.

Leon R. McCulloh (1987)

Journal für die reine und angewandte Mathematik

Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$

Elder Gove Griffith (1998)

Annales de l'institut Fourier

Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^{2}$

Gove Griffith Elder (1995)

Annales de l'institut Fourier

For $L / K$ , any totally ramified cyclic extension of degree $p^{2}$ of local fields which are finite extensions of the field of $p$ -adic numbers, we describe the $ℤ_{p} [Gal (L / K)]$ -module structure of each fractional ideal of $L$ explicitly in terms of the $4 p + 1$ indecomposable $ℤ_{p} [Gal (L / K)]$ -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

Galois Module Structure of Rings of Intergers.

Martha Rzedowski Calderón (1990)

Mathematische Zeitschrift

Galois representations

Richard Taylor (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Galois representations of dihedral type over ℚₚ

Peder Frederiksen, Ian Kiming (2004)

Acta Arithmetica

Galois structure of ideals in wildly ramified abelian $p$ -extensions of a $p$ -adic field, and some applications

Nigel P. Byott (1997)

Journal de théorie des nombres de Bordeaux

Let $K$ be a finite extension of $ℚ_{p}$ with ramification index $e$ , and let $L / K$ be a finite abelian $p$ -extension with Galois group $Γ$ and ramification index $p^{n}$ . We give a criterion in terms of the ramification numbers $t_{i}$ for a fractional ideal $𝔓^{h}$ of the valuation ring $S$ of $L$ not to be free over its associated order $𝔄 (K Γ; 𝔓^{h})$ . In particular, if $t_{n} - [t_{n} / p] < p^{n - 1} e$ then the inverse different can be free over its associated order only when $t_{i} \equiv - 1$ (mod $p^{n}$ ) for all $i$ . We give three consequences of this. Firstly, if $𝔄 (K Γ; S)$ is a Hopf order and $S$ is $𝔄 (K Γ; S)$ -Galois...