Search results for "Galois extension"

showing 4 items of 4 documents

Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus

2014

Let Y be a smooth, projective, irreducible complex curve. A G-covering p : C → Y is a Galois covering, where C is a smooth, projective, irreducible curve and an isomorphism G ∼ −→ Aut(C/Y ) is fixed. Two G-coverings are equivalent if there is a G-equivariant isomorphism between them. We are concerned with the Hurwitz spaces H n (Y ) and H G n (Y, y0). The first one parameterizes Gequivalence classes of G-coverings of Y branched in n points. The second one, given a point y0 ∈ Y , parameterizes G-equivalence classes of pairs [p : C → Y, z0], where p : C → Y is a G-covering unramified at y0 and z0 ∈ p (y0). When G = Sd one can equivalently consider coverings f : X → Y of degree d with full mon…

Discrete mathematicsHurwitz quaternionHurwitz space Galois covering Braid groupGalois cohomologyInverse Galois problemGeneral MathematicsGalois groupSplitting of prime ideals in Galois extensionsEmbedding problemCombinatoricsHurwitz's automorphisms theoremGalois extensionSettore MAT/03 - GeometriaMathematics
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A-Codes from Rational Functions over Galois Rings

2006

In this paper, we describe authentication codes via (generalized) Gray images of suitable codes over Galois rings. Exponential sums over these rings help determine--or bound--the parameters of such codes.

Discrete mathematicsMathematics::Commutative AlgebraApplied MathematicsFundamental theorem of Galois theoryGalois groupRational functionExponential polynomialComputer Science ApplicationsEmbedding problemDifferential Galois theorysymbols.namesakeGalois rings Gray map codesComputer Science::Computer Vision and Pattern RecognitionComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science::MultimediasymbolsSettore MAT/03 - GeometriaGalois extensionResolventMathematicsDesigns, Codes and Cryptography
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Hurwitz spaces of Galois coverings of P1, whose Galois groups are Weyl groups

2006

Abstract We prove the irreducibility of the Hurwitz spaces which parametrize equivalence classes of Galois coverings of P 1 , whose Galois group is an arbitrary Weyl group, and the local monodromies are reflections. This generalizes a classical theorem due to Luroth, Clebsch and Hurwitz.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryGalois cohomologyMathematics::Number TheoryFundamental theorem of Galois theoryGalois groupGalois moduleDifferential Galois theoryEmbedding problemsymbols.namesakeMathematics::Algebraic GeometryHurwitz's automorphisms theoremsymbolsGalois extensionMathematicsJournal of Algebra
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Multiplicities of fields of values of irreducible characters of finite groups

2021

We show that if f f is the largest multiplicity of the fields of values of the irreducible characters of a finite group G G , then | G | |G| is bounded from above in terms of f f .

Pure mathematicsApplied MathematicsGeneral MathematicsGalois extensionMathematicsProceedings of the American Mathematical Society
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