Factorisability and wildly ramified Galois extensions

David J. Burns

Displaying similar documents to “Factorisability and wildly ramified Galois extensions”

Factorisability and the arithmetic of wildly ramified Galois extensions

D. J. Burns (1989)

Journal de théorie des nombres de Bordeaux

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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 $L / ℚ$ .

The cyclic subfield integer index

Bart de Smit (2000)

Journal de théorie des nombres de Bordeaux

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In this note we consider the index in the ring of integers of an abelian extension of a number field $K$ of the additive subgroup generated by integers which lie in subfields that are cyclic over $K$ . This index is finite, it only depends on the Galois group and the degree of $K$ , and we give an explicit combinatorial formula for it. When generalizing to more general Dedekind domains, a correction term can be needed if there is an inseparable extension of residue fields. We identify this correction...

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...

Comparing orders of Selmer groups

Sébastien Bosca (2005)

Journal de Théorie des Nombres de Bordeaux

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Using both class field and Kummer theories, we propose calculations of orders of two Selmer groups, and compare them: the quotient of the orders only depends on local criteria.

Dihedral extensions of Q of degree 21 which contain non-Galois extensions with class number not divisible by l

Kiyoaki Iimura (1979)

Acta Arithmetica

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On the Iwasawa invariants of certain $ℤ_{p}$ -extensions

J. Carroll, H. Kisilevsky (1983)

Compositio Mathematica

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Some results on local fields

Akram Lbekkouri (2013)

Annales UMCS, Mathematica

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Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.