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 ( n 9 ) 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 , ⋯ ) contains infinite squarefree integers whenever 1 < c < 61 36 = 1 . 6944 ⋯ , 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...

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.