Thesis (doctoral)--Universität, Bayreuth, 2000.

Thesis supervisor: Frederick M. Goodman. Includes bibliographic references (p. 84-88).

Orientador: Antonio José Engler / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T22:18:49Z (GMT). No. of bitstreams: 1 Matos_FabioAlexandrede_D.pdf: 1117786 bytes, checksum: ce8cedb8cf95de8f81d4d520e2d308ad (MD5) Previous issue date: 2014 / Resumo: Apresentaremos neste trabalho um estudo sobre a aritmética corpos de característica distinta de 2 com um número finito de classes de quadrados. Dividido em duas partes, começaremos com um estudo do radical de Kaplansky de um corpo F e seu comportamento em 2-extensões de F. Na segunda parte introduziremos um novo objeto, as bases distinguidas, e exploraremos suas propriedades obtendo uma generalização do Teorema 90 de Hilbert, versão para o radical de Kaplansky, e propriedades cohomológicas de corpos que possuam base distinguida / Abstract: We will present in this work a study about the arithmetic of fields of characteristic different from 2 with a finite number of square class. Divided in two parts, we will start with a study of the Kaplansky¿s radical of a field F and its behavior in 2-extensions of F. In the second part will introduce a new object, the distinguished bases, and we will explore its properties obtaining a generalization of Hilbert¿s Theorem 90 for the Kaplansky's radical and cohomological properties of fields that own distinguished basis / Doutorado / Matematica / Doutor em Matemática

Dans cette thèse, on s’intéresse à des propriétés arithmétiques des variétés algébriques. Elle contient deux parties : partie géométrique (sur un corps quelconque) et partie arithmétique (sur un corps de nombres). Dans la partie géométrique, j’étudie le quotient par sa partie constante du troisième groupe de cohomologie non ramifiée des surfaces (géométriquement) rationnelles et de leurs torseurs universels. Pour les surfaces de del Pezzo de degré au moins 5, je montre que ce quotient est trivial, sauf pour des surfaces de del Pezzo de degré 8 d’un type particulier. Pour les torseurs universels ci-dessus, je montre que ce quotient est fini et je donne une condition suffisante pour qu’il soit nul, en termes de la structure galoisienne du groupe de Picard géométrique de la surface. Dans la partie arithmétique, on étudie l’obstruction de Brauer–Manin à l’approximation forte. En collaboration avec C. Demarche et F. Xu, nous établissons l’équivalence de l’obstruction de Brauer-Manin étale et de l’obstruction de descente pour les variétés quasi-projectives. Ensuite, j’établis un théorème très général sur l’approximation forte pour les variétés ouvertes munies d’une action d’un groupe linéaire connexe G et dont un ouvert est un espace homogène de G. / In this Ph.D. thesis, we investigate some arithmetic properties of algebraic varieties. The thesis consists of two parts: a geometric part (over an arbitrary field) and an arithmetic part (over a number field). The geometric part is devoted to the study of the quotient by its constant part of the third unramified cohomology group of (geometrically) rational surfaces and of their universal torsors. For del Pezzo surfaces of degree at least 5, we show that this quotient is zero, except in the case of del Pezzo surfaces of degree 8 of a special type. For universal torsors as above, we show this quotient is finite and we give a sufficient condition for it to vanish. This condition involves the Galois structure of the geometrical Picard group. The arithmetic part is devoted to the study of the Brauer-Manin obstruction to strong approximation. In collaboration with C. Demarche and F. Xu, we establish the equivalence of étale Brauer-Manin obstruction and the descent obstruction. Then I establish a general theorem about strong approximation of open varieties equipped with an action of a connected linear algebraic group G and containing a G-homogeneous space as open subset.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 106-107). Available also in a digital version from Dissertation Abstracts.

Not available / text

In this thesis, we study the representation theory of Lie colour algebras. Our strategy follows the work of G. Benkart, C. L. Shader and A. Ram in 1998, which is to use the Brauer algebras which appear as the commutant of the orthosymplectic Lie colour algebra when they act on a k-fold tensor product of the standard representation. We give a general combinatorial construction of highest weight vectors using tableaux, and compute characters of the irreducible summands in some borderline cases. Along the way, we prove the RSK-correspondence for tableaux and the PBW theorem for Lie colour algebras.

Made available in DSpace on 2014-06-12T18:28:44Z (GMT). No. of bitstreams: 2 arquivo4374_1.pdf: 611135 bytes, checksum: 2535337805c3894ff5d22fc566c01f86 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2008 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação tratamos alguns aspectos da teoria das formas quadráticas sobre um corpo, das álgebras com divisão e das álgebras centrais simples. Objetos importantes estudados são o anel de Witt, o grupo de Brauer, as álgebras de Clifford e o teorema de Wedderburn sobre a estrutura das álgebras centrais simples. Essas teorias são profundamente ligadas entre si e tem conexões com outras áreas como a teoria dos corpos, a geometria algébrica, a topologia algébrica, a teoria das representações e a física teórica. Matemáticos ilustres como Brauer, Clifford, Emmy Noether, Gauss, Hamilton, Hasse, Hurwitz e Wedderburn trabalharam nos temas detalhados nesta dissertação

No description available.