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Showing 1 to 20 of 125 for “"Galois"”.
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Quasicategorical Galois theories
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Calculation of Galois groups
<p>In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory …
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The Absolute Galois Group of the Rationals, Grothendieck's Dessin D'Enfants, and Galois Invariants
… a highly non-trivial action of the absolute Galois group of the rationals on a collection of relatively simple combinatorial objects. We then analyze recent work by Girondo, Gonzalez-Diez, Hidalgo, and Jones which provides two new Galois invariants for dessins called ''Zapponi orientability" …
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A Survey of Galois Theory
In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem …
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Galois Groups With Restricted Ramification
U of I Only
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Topics in Inverse Galois Theory
Galois theory, the study of the structure and symmetry of a polynomial or associated field extension, is a standard tool for showing the insolvability of a quintic equation by radicals. On the other hand, the Inverse Galois Problem, given a finite group G, find a finite extension of the rational …
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Galois 2 Groups Unramified Outside 2
Finally, we look at some nonabelian, real, Galois extensions K of Q , such that GK(2) is not free but has a free subgroup of index 2. In particular we focus on finite split metacyclic extensions and again we explicitly describe the structure of G K(2).
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Deformations of Three-Dimensional Galois Representations
Having explicitly calculated universal deformations, the next logical question is whether we can calculate deformations with local restrictions. In fact, the ordinary deformation problem is representable, and we explain how to calculate the universal ordinary deformation. We proceed to perform this …
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Steinitz Classes of Relative Galois Extensions
Made available in DSpace on 2014-12-09T22:17:56Z (GMT). No. of bitstreams: 1 7021010.pdf: 2149632 bytes, checksum: c0f60a71b8030ee8d0be140d4837db79 (MD5) Previous issue date: 1970
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Families of p̳-adic Galois representations
… and then apply it to the generic fibers of Galois deformation spaces. I study the finite slope deformation rings in details by computing the dimensions of their Zariski cotangent spaces via Galois cohomologies. It turns out that the Galois cohomologies tell us not only the formal smoothness …
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Galois representations of orthogonal rigid local systems
… can be specialized to compatible systems of Galois representations. This leads to the second maximally unipotent family. Because of the geometric origin, we can show using a theorem of Barnet-Lamb, Gee, Geraghty and Taylor that they are potentially automorphic.
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Topics in categorical algebra and Galois theory
… then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category by making use of the notions of admissibility and effective descent. We show that the admissibility of a functor can be extended to the …
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Extensive categories, commutative semirings and Galois theory
We describe the Galois theory of commutative semirings as a Boolean Galois theory in the sense of Carboni and Janelidze. Such a Galois structure then naturally suggests an extension to commutative semirings of the classical theory of quadratic equations over commutative rings. We show, however, …
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Subespacios de Galois para la curva racional normal.
… sobreyectivo. Diremos que W es un sub espacio de Galois para νn si π es un cubrimiento de Galois. Lo que se hará en este trabajo es caracterizar a todos los subespacios de Galois para la inmersión de Veronese νn. Se dará una descripción de estos subespacios como una unión disjunta de subvariedades …
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On the Inverse Problem in Differential Galois Theory
Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the …
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Lifting Galois Representations in a Conjecture of Figueiredo
… odd irreducible representations of the absolute Galois group of Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible representations of the absolute Galois group of M and their correspondence to homology classes. …
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An Equal-Distribution Result for Galois Module Structure
… be a fixed finite group. If K$\sb\pi$ is a tame Galois G-extension, the integral closure ${\cal O}\sb\pi$ of o in K$\sb\pi$ is a locally free rank one oG-module, so realizes a class cl(${\cal O}\sb\pi$) in the locally free class group Cl(oG). We let R(oG) denote the set of classes so realized. In …
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i = Galois : a fictional biography of the French mathematician Evariste Galois (1811-1832) : together with a methodological introduction and select bibliography
… on the French mathematical prodigy Evariste Galois (1811 -1832). After thoroughly researching and reading all the English sources, together with translations of material in French, it was found that most biographers presented a sketchy, two-dimensional picture of Galois. These biographies …
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