L’algèbre de Witt a été intensivement étudiée. Elle est présente dans de nombreux domaines des Mathématiques. Cette thèse est l’étude de deux généralisations de l’algèbre de Witt: les algèbres de type Witt et les algèbres de Krichever-Novikov. Dans une première partie on s’intéresse aux structures Lie-admissibles sur les algèbres de type Witt. On donne toutes les structures troisième-puissance associatives et flexibles Lie-admissibles sur ces algèbres. De plus, on étudie les formes symplectiques qui induisent un produit symétrique gauche. Dans une seconde partie on étudie les algèbres automorphes. Partant d’une surface de Riemann compacte quelconque, on considère l’action d’un sous-groupe fini du groupe des automorphismes de la surface sur des algèbres d’origines géométriques comme les algèbres de Krichever-Novikov. Plus précisément nous faisons le lien entre la sous-algèbre des éléments invariants sur la surface et l’algèbre sur la surface quotient. La structure presque-gradue des algèbres de Krichever-Novikov induit une presque-graduation sur ces sous-algèbres de certaines algèbres de Krichever- Novikov / The Witt algebra has been intensively studied and arise in many research fields in Mathematics. We are interested in two generalizations of the Witt algebra: the Witt type algebras and the Krichever-Novikov algebras. In a first part we study the problem of finding Lie-admissible structures on Witt type algebras. We give all third-power associative Lie-admissible structures and flexible Lie-admissible structures on these algebras. Moreover we study the symplectic forms which induce a graded left-symmetric product. In the second part of the thesis we study the automorphic algebras. Starting from arbitrary compact Riemann surfaces we consider the action of finite subgroups of the automorphism group of the surface on certain geometrically defined Lie algebras as the Krichever-Novikov type algebras. More precisely, we relate for G a finite subgroup of automorphism acting on the Riemann surface, the invariance subalgebras living on the surface to the algebras on the quotient surface under the group action. The almost-graded Krichever-Novikov algebras structure on the quotient gives in this way a subalgebra of a certain Krichever-Novikov algebra (with almost-grading) on the original Riemann surface

Denna uppsats behandlar Stina Aronsons Feberboken - stoffet till en roman (1931) i syftet att ifrågasätta verkets status som självbiografiskt dokument. Uppsatsen innehåller en komparativ analys av karaktären Hugos brevutdrag i Feberboken och de autentiska brev från Artur Lundkvist som står som förlaga till den fiktiva brevkorrespondensen. Analysen resulterar i att tidigare forsknings jämställande av Hugo och den verklige personen Artur Lundkvist framstår felaktig, och slutdiskussionen rymmer en dialog med representanter för den vedertagna läsningen av verket.

Bibliography: pages 325-334. / This thesis is a theological and historical study of the Swedish missionary and evangelist Peter Otto Helger Witt (1848-1923), who served as the Church of Sweden Mission's first missionary and as such launched its work amongst the Zulu people of Southern Africa in the 1870S before growing disillusioned with his national Lutheran tradition and, after following a tortuous spiritual path through generally increasing theological subjectivity, eventually becoming a loosely affiliated Pentecostal evangelist in Scandinavia. Undoubtedly owing to the embarrassment he caused the Church of Sweden Mission by resigning from it while it was in a formative stage, but also to tension between him and its leaders, Witt has never received his due in the historiography of Swedish missions. For that matter, his role in Scandinavian nonconformist religious movements for nearly a third of a century beginning in the early 1890S is a largely untold chapter in the ecclesiastical history of the region. This thesis is intended to redress these lacunae by presenting Witt's career as both a foreign missionary and evangelist as well as the contours of his evolving religious thought and placing both of these emphases into the broader history of Scandinavian and other missionary endeavours amongst the Zulus, late nineteenth-century developments in Swedish Lutheranism, and the coming to northern Europe of those religious movements in which he successively became involved. As the copious documentation indicates, it is based to a great extent on little-used materials in the archives of the Church of Sweden Mission and other repositories in Scandinavia, South Africa, and the United States of America. Witt's own numerous publications also provide much of the stuff for it. The structure of this study is essentially chronological and, within that framework, thematic with clear precedents in previous missions and ecclesiastical historiography. The first chapter is largely a critical review of previous pertinent literature, professional and otherwise, emphasising its general misunderstanding and neglect of Witt. Chapter II covers his background in nineteenth-century Swedish Lutheranism, call to the Church of Sweden Mission, and role in establishing that organisation's endeavours amongst the Zulus. Chapter Ill deals with the trauma of the Anglo-Zulu War of 1819, particularly Witt's controversial but misunderstood role in it and the place of this in the existing historiography of that conflagration. Chapter IV surveys his part in re-establishing the Swedish Lutheran mission following the war and his co-operative and at times creative role in this major task. Chapters V and VI, on the other hand, have as their respective themes Witt's consequential spiritual crisis of the mid-1880s and resulting gradual departure from the Church of Sweden Mission. The seventh chapter is a consideration of Witt's Participation in and temporarily great impact on the Free East Africa Mission, a pan-Scandinavian free church undertaking which undertook evangelisation in both Durban and rural Natal in 1889. Chapter VIII treats Witt's generally independent career in Scandinavia from 1891 until his death, focusing on the new developments in which he became involved. The final chapter is an attempt to assess his general place in the missions and ecclesiastical history of Scandinavia and Southern Africa.

We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a bialgebra. For the proof we need some facts from the theory of ring schemes where we extend previously known results. We also classify plethories with trivial Verschiebung over a perfect field of non-zero characteristic and indicate future work. / <p>QC 20151117</p>

Soient G un groupe fini et k un corps dont la caractéristique ne divise pas l’ordre de G. Il est établi, d’une part que pour que tous les caractères irréductibles de G soient réels, il faut et il suffit que G soit ambivalent; d’autre part, que pour que la restriction de l’involution canonique à chaque composante simple de l’algèbre de groupe kG soit une involution de première espèce, il faut et il suffit que G soit ambivalent. G est dit ortho-ambivalent par rapport à k si la restriction de l’involution canonique à chaque composante simple de l’algèbre de groupe kG est une involution orthogonale. Dans cette thèse, nous démontrons que les propositions suivantes sont équivalentes : (i) G est ortho-ambivalent par rapport à k ; (ii) G est totalement orthogonal ; (iii) G est ambivalent et tout caractère irréductible de G est de type 1 ; (iv) G est ambivalent et la somme des degrés des caractères irréductibles de G égale le nombre d’éléments de G dont les carrés sont égaux à l’élément neutre de G ; de plus, si la caractéristique de k est différente de 2, ces propositions sont équivalentes à la suivante : (v) G est ambivalent et le premier groupe de Witt tordu de la catégorie des kG-modules libres finiment engendrés munie d’une dualité définie en fonction de l’involution canonique sur kG est trivial. L’étude des 2-groupes spéciaux occupe une partie importante. Nous démontrons qu’un 2-groupe spécial ambivalent G d’application quadratique q est ortho-ambivalent par rapport à k si et seulement si pour toute forme linéaire s sur le centre de G (par rapport au corps à 2 éléments), l’invariant d’Arf de la forme quadratique induite par le transfert de q par s est nul. / Let G be a finite group and k a field whose characteristic does not divide the order of G. It is established, on the one hand that all irreducible characters of G are real if and only if G is ambivalent; in addition, that the restriction of the canonical involution on each simple component of the group algebra kG is an involution of first kind if and only if G is ambivalent. We say that G is ortho-ambivalent compared to k if the restriction of the canonical involution on each simple component of the group algebra kG is an orthogonal involution. In this thesis, we show that the following conditions are equivalent: (I) G is ortho-ambivalent compared to k; (II) G is totaly orthogonal; (III) G is ambivalent and any irreducible character of G is of type 1; (iv) G is ambivalent and the sum of the degrees of the irreducible characters of G equalizes the number of elements of G whose squares are equal to the neutral element of G; moreover, if the characteristic of k is different from 2, these conditions are equivalent to the following one: (v) G is ambivalent and the first twisted Witt group of the category of the free kG-modules finitely generated provided with a duality defined according to the canonical involution on kG is trivial. The study of the special 2-groups occupies a great part. We show that an ambivalent special 2-group G of quadratic application q is ortho-ambivalent compared to k if and only if for any linear form s on the center of G (compared to the field with 2 elements), the Arf invariant of the quadratic form induced by the transfer of q by s is null.

Neste trabalho procuramos realizar uma apresentação autocontida sobre os conceitos da teoria algébrica de formas quadráticas e sobre os anéis graduados que surgiram no desenvolvimento desta teoria. Iniciamos procurando esclarecer o sentido da equivalência entre as várias acepções do conceito de forma quadrática. Após a apresentação de ingredientes e resultados geométricos, fazemos um extrato da teoria dos anéis de Witt, conceito que originou a moderna teoria algébrica de formas quadráticas. Disponibilizamos os elementos fundamentais para a formulação das teorias de cohomologia, nos concentrado no desenvolvimento da teoria de cohomologia profinita e, sobretudo, galoisiana. Descrevemos os funtores K0, K1 e K2 da K-teoria clássica e também a K-teoria de Milnor, que é mais adequada para formular questões sobre formas quadráticas. Finalizamos o trabalho com a apresentação de alguns conceitos da Teoria dos Grupos Especiais, uma codificação em primeira-ordem da teoria algébrica das formas quadráticas e exemplificamos sua importância, fornecendo um extrato da prova realizada por Dickmann-Miraglia da conjectura de Marshall sobre assinaturas, que se baseia fortemente nesta teoria. / In this work I try to provide a self-contained presentation on the concepts of algebraic theory of quadratic forms and on the graded rings that have emerged in the development of this theory. I started trying to clarify the meaning of \"equivalence\"between the various meanings of the concept of quadratic form. After the presentation of geometrical ingredients and results, we make an extract of the theory of Witt rings, a concept that originated the modern algebraic theory of quadratic forms. It is provided the key elements for the formulation of cohomology theories, focusing on the development of profinite cohomology theory and, especially, on galoisian cohomology. Are described the functors K0, K1 and K2 of classical K-theory and also the Milnor K-theory, which is more appropriate to formulate questions about quadratic forms. The dissertation is finished with the presentation of some concepts of the Theory of Special Groups, a first-order encoding of algebraic theory of quadratic forms, and with an example its importance by providing an extract of proof by Dickmann-Miraglia of the Marshalls conjecture on signatures, which relies heavily on this theory.

O objetivo deste texto é apresentar uma classe de módulos para álgebra de Lie de campos vetoriais em um toro N -dimensional, Vect( T N ). O caso N = 1 nos dá a famosa álgebra de Witt (sua extensão central é álgebra de Virasoro). A álgebra Vect( T N ) apresenta um classe de módulos parametrizada por módulos de dimensão finita da álgebra gl N . Nosso objeto central de estudo são módulos induzidos dos módulos tensoriais de Vect( T N ) para Vect( T N +1 ). Estes módulos apresentam um quociente irredutível com espaços de peso de dimensão finita. A álgebra Vect( T N ) apresenta como subálgebra sl N +1 . Com a restrição da ação de Vect( T N ) a esta subálgebra obtemos o carácter deste quociente. Para obter um critério de irredutibilidade e construir sua realização de campo livre, consideramos uma classe de módulos para 1 (T N +1 )/ d 0 (T N +1 ) o Vect (T N ) , construída a partir de álgebras de vértice. Quando restritos a Vect (T N ) estes módulos continuam irredutíveis a menos que apareçam no chiral de De Rham. / The goal of this text is to present a class of modules for the Lie algebra of vector fields in a N -dimensional torus, Vect (T N ) . The case N = 1 give us the famous Witt algebra (its central extension is the Virasoro algebra). The algebra Vect( T N ) has a class of modules parametrized by finite dimensional gl N -modules. The central object of our study are modules induced from tensor modules for Vect( T N ) to Vect( T N +1 ). Those modules have an irreducible quotient such that every weight space has finite dimension. The algebra Vect( T N ) has as subalgebra sl N +1 . Restricting the action of Vect( T N ) to this subálgebra we have the character of this quotient. To obtain a irreducible critreria and construct a free field reazilation, we consider a class of modules for 1 (T N +1 )/ d 0 (T N +1 ) o Vect (T N ) , constructed from vertex algebras. When restricted to Vect (T N ) thesse modules remain irreducible, unless they belongs to the chiral De Rham complex.

Neste trabalho procuramos realizar uma apresentação autocontida sobre os conceitos da teoria algébrica de formas quadráticas e sobre os anéis graduados que surgiram no desenvolvimento desta teoria. Iniciamos procurando esclarecer o sentido da equivalência entre as várias acepções do conceito de forma quadrática. Após a apresentação de ingredientes e resultados geométricos, fazemos um extrato da teoria dos anéis de Witt, conceito que originou a moderna teoria algébrica de formas quadráticas. Disponibilizamos os elementos fundamentais para a formulação das teorias de cohomologia, nos concentrado no desenvolvimento da teoria de cohomologia profinita e, sobretudo, galoisiana. Descrevemos os funtores K0, K1 e K2 da K-teoria clássica e também a K-teoria de Milnor, que é mais adequada para formular questões sobre formas quadráticas. Finalizamos o trabalho com a apresentação de alguns conceitos da Teoria dos Grupos Especiais, uma codificação em primeira-ordem da teoria algébrica das formas quadráticas e exemplificamos sua importância, fornecendo um extrato da prova realizada por Dickmann-Miraglia da conjectura de Marshall sobre assinaturas, que se baseia fortemente nesta teoria. / In this work I try to provide a self-contained presentation on the concepts of algebraic theory of quadratic forms and on the graded rings that have emerged in the development of this theory. I started trying to clarify the meaning of \"equivalence\"between the various meanings of the concept of quadratic form. After the presentation of geometrical ingredients and results, we make an extract of the theory of Witt rings, a concept that originated the modern algebraic theory of quadratic forms. It is provided the key elements for the formulation of cohomology theories, focusing on the development of profinite cohomology theory and, especially, on galoisian cohomology. Are described the functors K0, K1 and K2 of classical K-theory and also the Milnor K-theory, which is more appropriate to formulate questions about quadratic forms. The dissertation is finished with the presentation of some concepts of the Theory of Special Groups, a first-order encoding of algebraic theory of quadratic forms, and with an example its importance by providing an extract of proof by Dickmann-Miraglia of the Marshalls conjecture on signatures, which relies heavily on this theory.

Orientador: Marcos Benevenuto Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T16:48:31Z (GMT). No. of bitstreams: 1 Cardoso_NunoFilipedeAndrade_M.pdf: 1858794 bytes, checksum: bbe47182338feb3de60b480df87b52a7 (MD5) Previous issue date: 2014 / Resumo: Os teoremas de degenerescência de Hodge e de anulamento de Kodaira, Akizuki e Nakano são de suma importância na teoria de variedades complexas. Usando o teorema de comparação de Serre, ambos podem ser traduzidos para o contexto de esquemas projetivos e suaves sobre um corpo de característica zero. Para corpos de característica positiva, no entanto, os dois deixam de valer sem hipóteses adicionais, sendo que os primeiros contra-exemplos foram encontrados por Mumford e Raynaud. O objetivo desta dissertação é apresentar um teorema devido a Deligne e Illusie que assegura a degenerescência da seqüência espectral de Hodge-de Rham e uma versão do teorema de Kodaira, Akizuki e Nakano para certos esquemas projetivos e suaves sobre um corpo perfeito de característica positiva. Nos propusemos a dar um tratamento, na medida do possível, auto-suficiente / Abstract: The Hodge degeneration theorem and the Kodaira, Akizuki and Nakano's vanishing theorem are of paramount importance in the theory of complex manifolds. Using Serre's comparison theorem, both can be translated to the context of smooth projective schemes over a field of characteristic zero. For fields of positive characteristic, however, both fail to hold without additional hypothesis, and the first counterexamples were found by Mumford and Raynaud. Our goal in this dissertation is to present a theorem due to Deligne and Illusie that ensures the degeneration of the Hodge-de Rham spectral sequence and a version of the theorem of Kodaira, Akizuki and Nakano for certain smooth projective schemes over a perfect field of positive characteristic. We tried to keep the treatment as self-contained as possible / Mestrado / Matematica / Mestre em Matemática

Soit k un corps algébriquement clos de caractéristique p>0. Soit C/k une courbe algébrique, propre, lisse et de genre g>1, munie d'un p-groupe G d'automorphismes tel que |G|/g> 2p/(p-1). Un tel couple (C,G) est appelé une "grosse action". Sous ces hypothèses, C--> C/G est un revêtement étale de la droite affine Spec k[X], complètement ramifié à l'infini. Après avoir précisé certaines propriétés du deuxième groupe de ramification G_2 de G à l'infini, on donne des exemples de telles actions avec G_2 abélien d'exposant quelconque. Ces exemples trouvent leur source dans la construction , via les corps de classes de rayon, de courbes algébriques sur un corps fini possédant beaucoup de points rationnels. On se concentre ensuite sur le cas où G_2 est un p-groupe abélien élémentaire. En considérant une filtration d'anneau de k[X] liée aux polynômes additifs, on obtient un théorème de structure pour les fonctions paramétrant le revêtement d'Artin-Schreier: C --> C/G_2. On exhibe alors des familles universelles et on discute l'espace de déformation correspondant lorsque p=5. On déduit de ces résultats une classification et une paramétrisation de telles actions lorsque |G|/g^2 est supérieur ou égal à 4/(p^2-1)^2. / Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g>1. We define a big action as a pair (C,G) where G is a p-subgroup of the k-automorphism group of C such that |G| /g > 2p / p-1. Then, C ---> C/G is an étale cover of the affine line Spec k[X] totally ramified at infinity. We first give necessary conditions on the second ramification G_2 of G at infinity for (C,G) to be a big action. We also display realizations of such actions with G_2 abelian of exponent as large as we want. Our main source of examples comes from the construction of curves with many rational points using ray class field theory for global function fields. Then we focus on the case where G_2 is p-elementary abelian. In particular, considering additive polynomials of k[X], we obtain a structure theorem for the functions parametrizing the Artin-Schreier cover C --> C/G_2. Then we display universal families and discuss the corresponding deformation space for p=5. All these results lead to the classification and the parametrization of big actions for |G|/g^2 greater or equal to 4/(p^2-1)^2.