Displaying similar documents to “Quaternion extensions with restricted ramification”

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let L be a Galois extension of a countable Hilbertian field K . Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L / K are.

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

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For each transitive permutation group G on n letters with n ≤ 4 , we give without proof results, conjectures, and numerical computations on discriminants of number fields L of degree n over ℚ such that the Galois group of the Galois closure of L is isomorphic to G .

Galois towers over non-prime finite fields

Alp Bassa, Peter Beelen, Arnaldo Garcia, Henning Stichtenoth (2014)

Acta Arithmetica

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We construct Galois towers with good asymptotic properties over any non-prime finite field ℓ ; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over ℓ of increasing genus, such that all the extensions N i / N 1 are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with...

Differential Galois Theory for an Exponential Extension of ℂ ( ( z ) )

Magali Bouffet (2003)

Bulletin de la Société Mathématique de France

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In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of ℂ ( ( z ) ) by an exponential of integral. We use results of factorization of differential operators with coefficients in such a field to give explicit generators of the Galois group. We show that we have very similar results to the case of ℂ ( ( z ) ) .

An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

Amit Hogadi, Supriya Pisolkar (2013)

Acta Arithmetica

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Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension k L / k K is separable. For an integer n ≥ 0, let W n ( L ) denote the ring of Witt vectors of length n with coefficients in L . We show that the proabelian group H 1 ( G , W n ( L ) ) n ∈ ℕ is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.

A characterization of Eisenstein polynomials generating extensions of degree p 2 and cyclic of degree p 3 over an unramified 𝔭 -adic field

Maurizio Monge (2014)

Journal de Théorie des Nombres de Bordeaux

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Let p ≠ 2 be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree p 2 over ℚ p , and extend it to when the base fields K is an unramified extension of ℚ p . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We...

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

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Fix an integer ℓ ≥ 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order ℓ , where K satisfies some mild hypotheses. In this paper we define the family of { r n ( x , t ) } n ≥ 1 of degree ℓ n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd ℓ over an arbitrary base field and give applications to arithmetic dynamical systems.