Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$

Filippo Viviani

Displaying similar documents to “Ramification groups and Artin conductors of radical extensions of $ℚ$ ”

On the $n$ -torsion subgroup of the Brauer group of a number field

Hershy Kisilevsky, Jack Sonn (2003)

Journal de théorie des nombres de Bordeaux

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Given a number field $K$ Galois over the rational field $ℚ$ , and a positive integer $n$ prime to the class number of $K$ , there exists an abelian extension $L / K$ (of exponent $n$ ) such that the $n$ -torsion subgroup of the Brauer group of $K$ is equal to the relative Brauer group of $L / K$ .

Pure fields of degree 9 with class number prime to 3

Colin D. Walter (1980)

Annales de l'institut Fourier

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The main theorem gives necessary conditions and sufficient conditions for $Q (\sqrt[9]{n})$ to have class number prime to 3. These conditions involve only the rational prime factorization of $n$ and congruences mod 27 of the prime factors of $n$ . They give necessary and sufficient conditions for most $n$ .

The distribution of square-free numbers of the form $[n^{c}]$

Xiaodong Cao, Wenguang Zhai (1998)

Journal de théorie des nombres de Bordeaux

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It is proved that the sequence $[n^{c}] (n = 1, 2, \dots)$ contains infinite squarefree integers whenever $1 < c < \frac{61}{36} = 1.6944 \dots$ , which improves Rieger’s earlier range $1 < c < 1.5$ .

New ramification breaks and additive Galois structure

Nigel P. Byott, G. Griffith Elder (2005)

Journal de Théorie des Nombres de Bordeaux

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Which invariants of a Galois $p$ -extension of local number fields $L / K$ (residue field of char $p$ , and Galois group $G$ ) determine the structure of the ideals in $L$ as modules over the group ring $ℤ_{p} [G]$ , $ℤ_{p}$ the $p$ -adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups $G$ , we propose and study a new group (within the group ring $𝔽_{q} [G]$ where $𝔽_{q}$ is the residue field) and its resulting ramification...

A construction of unramified Abelian l-extensions of regular Kummer extensions

Norikata Nakagoshi (1984)

Acta Arithmetica

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Factorisability and wildly ramified Galois extensions

David J. Burns (1991)

Annales de l'institut Fourier

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Let $L / K$ be an abelian extension of $p$ -adic fields, and let $𝒪$ denote the valuation ring of $K$ . We study ideals of the valuation ring of $L$ as integral representations of the Galois group $Gal (L / K)$ . Assuming $K$ is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an $𝒪$ -order in the group algebra $K [Gal (l / K)]$ . We obtain several general and also explicit new results.

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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Displaying similar documents to “Ramification groups and Artin conductors of radical extensions of ℚ ”

On the n -torsion subgroup of the Brauer group of a number field

Pure fields of degree 9 with class number prime to 3

The distribution of square-free numbers of the form [ n c ]

New ramification breaks and additive Galois structure

A construction of unramified Abelian l-extensions of regular Kummer extensions

Factorisability and wildly ramified Galois extensions

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

Displaying similar documents to “Ramification groups and Artin conductors of radical extensions of $ℚ$ ”

On the $n$ -torsion subgroup of the Brauer group of a number field

The distribution of square-free numbers of the form $[n^{c}]$