77 research outputs found
Points entiers, monodromie, annulation générique et la transformation de Fourier-Mukai
No full textCette thèse est une compilation de plusieurs résultats vaguement liés. Ils concernent la non-densité des points entiers sur les variétés algébriques, la méthode de Lawrence-Venkatesh-Sawin et la géométrie analytique complexe. Dans Chapitre 2, parallèlement au principe alternatif d'Ullmo et Yafaev sur les points rationnels des variétés de Shimura, nous montrons que la conjecture de Lang sur les points intégraux des variétés de Shimura est soit vraie, soit très fausse. Le Chapitre 3 est un complément à la comparaison des monodromies dans les travaux respectifs de Lawrence-Sawin et Krämer-Maculan. Nous prouvons qu'il existe de nombreux caractères, tels que le groupe de monodromie correspondant est normal dans le groupe tannakien générique. Le Chapitre 4 contient un théorème de l'annulation générique pour les variétés dans la classe Fujiki C. En particulier, cela s'applique aux variétés algébriques complexes propres lisses ainsi qu'aux variétés kählériennes compactes. Dans Chapitre 5, nous prouvons un analogue de la formule d'inversion de Fourier pour la transformation de Fourier-Mukai sur des tores complexes. Il corrige une inexactitude dans la littérature. En application, nous retrouvons la classification de Matsushima-Morimoto des fibrés vectoriels homogènes sur des tores complexes. Le Chapitre 6 est une transformation de Fourier-Mukai analytique sur les D-modules, dont la version algébrique a été étudiée par Laumon et Rothstein. Nous étendons leur résultat de dualité des variétés abéliennes aux tores complexes. En application, nous réprouvons le théorème de Morimoto, selon lequel sur un tore complexe, tout fibré vectoriel admettant une connexion admet une connexion intégrable.This dissertation is a compilation of several loosely related results.They concern the nondensity of integral points on algebraic varieties, the Lawrence-Venkatesh-Sawin's method and complex analytic geometry.In Chapter 2, parallel to Ullmo and Yafaev's alternative principle on rational points of Shimura varieties, we show that Lang's conjecture about integral points on Shimura varieties is either true or very false.Chapter 3 is a complement to the monodromy comparison step in Lawrence-Sawin's and Krämer-Maculan's respective work. We prove that there are many characters, such that the corresponding monodromy group is normal in the generic Tannakian group.Chapter 4 contains a generic vanishing theorem for Fujiki class C. In particular, it applies to smooth proper complex algebraic varieties as well as compact Kähler manifolds. In Chapter 5, we prove an analog of the Fourier inversion formula for the Fourier-Mukai transform on complex tori. It corrects a misstatement in the literature. As an application, we recover Matsushima-Morimoto's classification of homogeneous vector bundles on complex tori.Chapter 6 is a lift of the analytic Fourier-Mukai to D-modules, whose algebraic version is studied by Laumon and Rothstein. We extend their duality result from abelian varieties to complex tori. As an application, we reprove Morimoto's theorem that on a complex torus, every vector bundle admitting a connection admits a flat connection
Arithmetic aspects of period maps and their special subvarieties
No full textDiese Dissertation behandelt arithmetische Eigenschaften von Familien algebraischer Varietäten und deren speziellen Untervarietäten.
Im ersten Kapitel definieren wir sogenannte absolut spezielle Untervarietäten mithilfe von Delignes Begriff der absoluten Hodgeklassen.
Ausgehend von der Vermutung, dass alle Hodgeklassen absolute Hodgeklassen sind, erwarten wir, dass alle speziellen Untervarietäten absolut speziell sind.
Wir beweisen diese Erwartung für Untervarietäten, die eine bestimmte Monodromiebedingung erfüllen.
Das zweite Kapitel führt eine l-adische Version von speziellen Untervarietäten ein, die wir l-Galois spezielle Untervarietäten nennen. Wir studieren bewiesene und vermutete Eigenschaften dieser Untervarietäten und deren Zusammenhang zur Struktur des l-Galois exzeptionellen Locus und zur Mumford-Tate Vermutung.
Im dritten Kapitel beweisen wir eine Rapoport-Zink Uniformisierung für den Modulraum der primitiv polarisierten K3 Flächen und kubischen Vierfaltigkeiten mit supersingulärer Reduktion.
In beiden Fällen ist der Modulraum uniformisiert von einer explizit definierten rigid analytischen Untervarietät einer lokalen Shimura-Varietät von orthogonalem Typ.This thesis studies arithmetic aspects of families of algebraic varieties and their special subvarieties. In the first part, we use Deligne's framework of absolute Hodge classes to define a notion of absolutely special subvarieties.
The conjecture that all Hodge classes are absolute Hodge predicts that every special subvariety is absolutely special. We prove this prediction for subvarieties satisfying a certain monodromy condition.
The second part introduces an l-adic analog of special subvarieties that we call l-Galois special subvarieties.
We study the properties of these subvarieties and discuss how known and unknown properties of l-Galois special subvarieties are related to the structure of the l-Galois exceptional locus and to the Mumford-Tate conjecture.
In the third chapter, we prove a Rapoport-Zink type uniformization result for the moduli space of polarized K3 surfaces and cubic fourfolds. We show that in both cases, the tube over the supersingular locus of the moduli space is uniformized by an explicitly described rigid analytic open subvariety of a local Shimura variety of orthogonal type
Nós já somos uma família, só faltam os filhos: maternidade lésbica e novas tecnologuas reprodutivas no Brasil
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Filosofia e Ciências Humanas, Programa de Pós-Graduação em Antropologia Social, Florianópolis, 2013Esta etnografia busca apresentar reflexões preocupadas com a parentalidade homossexual e com as relações de parentesco forjadas e remodeladas através da reprodução assistida. Neste sentido, problematizo o modo como a conjugalidade homossexual, a homoparentalidade e as novas configurações familiares complexificam o debate que tange a reprodução assistida e o corrente entendimento do que seja natural na reprodução humana, nos obrigando, assim, a repensar as categorias básicas do nosso parentesco. Em sintonia, o interesse central desta pesquisa é a maneira como lésbicas que procuram por novas tecnologias reprodutivas estão construindo, remodelando, classificando e pensando o modelo estabelecido de parentesco, parentalidade e família. O esforço deste trabalho foi o de atar diferentes lados e ambigüidades a respeito da temática presente nas trajetórias de vida, discursos, notícias, blogs e comunidades de redes sociais. A possibilidade de não ver as relações sociais como uma via de mão única animaram este caminho. Destaco que a família homoparental não é apenas uma tentativa de assemelhar-se a um modelo vigente. É antes outra coisa, um processo complexo que necessita investigação já que as práticas parentais são mais que simples conseqüências dos valores do casal, estando sujeitas às pressões da rede familiar mais ampla, de colegas de trabalho e amigos. Tais desejos por filiação também são exemplares de uma estratégia coerente que visa dar à conjugalidade homossexual legitimidade perante a sociedade que continua materializando este arranjo familiar em um recorte stigmatizado. As interlocutoras deste trabalho são casais formados por mulheres lésbicas que procuram ou que já realizaram o procedimento de reprodução assistida <br
Motivic representations in positive characteristic
No full textThis is a brief report on the research achievements I obtained jointly with Akio Tamagawa during my stay at R.I.M.S. as a research fellow funded by the International Research Unit of Advanced Future Studies, Kyoto University. Period of the stay: June 6th, 2016--August 25th, 2016
Lifting results for rational points on Hurwitz moduli spaces
No full textHurwitz moduli spaces for G-covers of the pro jective line have two classical variants whether G- covers are considered modulo the action of PGL2 on the base or not. A central result of this paper is that, given an integer r ≥ 3 there exists a bound d(r) ≥ 1 depending only on r such that any rational point p rd of a reduced (i.e. modulo PGL2 ) Hurwitz space can be lifted to a rational point p on the non reduced Hurwitz space with [κ(p) : κ(prd )] ≤ d(r). This result can also be generalized to infinite towers of Hurwitz spaces. Introducing a new Galois invariant for G-covers, which we call the base invariant, we improve this result for G-covers with a non trivial base invariant. For the sublocus corresponding to such G-covers the bound d(r) can be chosen depending only on the base invariant (no longer on r) and ≤ 6. When r = 4, our method can still be refined to provide effective criteria to lift k-rational points from reduced to non reduced Hurwitz spaces. This, in particular, leads to a rigidity criterion, a genus 0 method and, what we call an expansion method to realize finite groups as regular Galois groups over Q. Some specific examples are given
On the profinite regular inverse Galois Problem
No full textGiven a field k, a k-curve X and a k-rational divisor t ⊂ X, we analyze the constraints imposed on X and t by the existence of abelian G-covers f : Y → X defined over k and unramified outside t. We show that these constraints produce an obstruction to the weak regular inverse Galois problem for a whole class of profinite groups - we call p-obstructed - when k is a finitely generated field of characteristic ̸= p
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