796 research outputs found
Structure theorems for non-Noetherian modules aimed at non-Noetherian Iwasawa theory
No full textTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Francesc Bars CortinaWe explore several structure theorems for modules over non-Noetherian rings, with a particular interest in finitely presented torsion modules. Our main objective is to prove structure theorems for admissible modules, a new class introduced by Burns et al. in [7]. This work intends to be mostly self-contained: a first chapter is devoted to fixing preliminaries, a second chapter is devoted to presenting some key homological results due to Endo [10] and to the proof of structure theorems for finitely presented torsion modules over EDR domains, valuation rings and Prüfer rings, the last two due to Warfield [28]. In the third and last chapter, we prove the classical structure theorem for Noetherian Krull domains, introduce admissible modules, and prove theorems describing their structure. Finally, we present an application to classical and non-Noetherian Iwasawa theory
Parodia y deporte en Quo Vadis, Sànchez?, de Francesc Trabal
No full textResumen:
El presente artículo tiene como objetivo estudiar la importancia de la parodia en Francesc Trabal a través del análisis de la novela Quo vadis Sànchez?, publicada en 1931. En primer lugar, se revisan las diferentes consideraciones que ha tenido la obra narrativa del autor por parte de la bibliografía precedente y, más adelante, se destaca la parodia como uno de los aspectos más relevantes que cabe considerar. Posteriormente, se describe el concepto de parodia y se analiza su efectividad en la novela trabaliana. Este análisis de la parodia en la novela de Trabal permite ver el juego de distanciamiento irónico de Trabal contra el modelo y los valores promovidos por la novela deportiva de la época.
Palabras clave: parodia, novela deportiva, Francesc Trabal, literatura catalana, ironía intertextual
Abstract:
The paper aims to study the importance of parody in Francesc Trabal through the analysis of the novel Quo Vadis, Sànchez?, published in 1931. Firstly, we examine the different considerations about the narrative work of the author shown in previous studies and, later, we underline parody as one of the most relevant aspects for examination. Subsequently, we describe the concept of parody and then we analyse its efficacy in this novel. The analysis of parody lets us understand Trabal’s game of ironic distance against the model and the values promoted by the sport novel from the period.
Keywords: parody, sport novel, Francesc Trabal, Catalan literature, intertextual irony
Aspects of Iwasawa theory over function fields
No full textWe consider -extensions of a global function field and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety defined over , we provide all the ingredients to formulate an Iwasawa Main Conjecture relating the Fitting ideal and the -adic -function associated to and . We do the same, with characteristic ideals and -adic -functions, in the case of class groups (using known results on characteristic ideals and Stickelberger elements for -extensions). The final section provides more details for the cyclotomic -extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli-Carlitz numbers by a Coates-Wiles homomorphism
Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
No full textWe prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero–Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i.e., on the values of the Carlitz-Goss ζ-function at negative integers)
Reconstrucción
No full textEn el presente porfolio se pretende, en primer lugar, mostrar la evolución personal del autor, Francesc Serrano. Como estudiante del grado de Arquitectura, mi paso por la universidad ha estado estrechamente vinculado con mi profesión; ambas con un desarrollo y aprendizaje retroalimentado.En el present portfoli es pretén, en primer lloc, mostrar l'evolució personal de l'autor, Francesc Serrano. Com a estudiant del grau d'Arquitectura, el meu pas per la universitat ha estat estretament vinculat amb la meva professió; totes dues amb un desenvolupament i aprenentatge retroalimentat.In this portfolio it is intended, first of all, to show the personal evolution of the author, Francesc Serrano. As a student of the Architecture degree, my time at the university has been closely linked to my profession; both with feedback development and learning
On the stratification of smooth plane curves by automorphism groups
No full textBibliografia.Premi Extraordinari de Doctorat concedit pels programes de doctorat de la UAB per curs acadèmic 2016-2017Curvas proyectivas no singulares sobre un cuerpo con grupo de automorfismo no trivial son de gran interés en Geometría Aritmética. En la tesis, estudiamos la estratificación de las curvas planas no singulares (de género mayor o igual a tres) por sus grupos de automorfismos y tratamos con aspectos de geometría algebraica y aritmética. En primer lugar, aportamos un estudio general de las clases (modulo -isomorfismo) de curvas planas lisas de género fijo g con un subgrupo de automorfismo fijo , donde denota una clausura algebraica fijada de . En particular, se aporta un estudio de grupos de automorfismos que aparecen y las ecuaciones definitorias asociadas en dichas clases. En segundo lugar, sea C una curva proyectiva lisa definida sobre , en particular por extensión de escalares obtenemos una curva lisa sobre y suponemos que dicha extension corresponde a una curva plana no singular. Nuestro objetivo es estudiar cuerpos de definición de modelos planos no singulares para y de sus ̀̀twists'' sobre , usando la inmersión en en lugar de la dada por el modelo canónico en . Más concretamente, preguntamos si es una curva plana lisa sobre o no; y si la respuesta es afirmativa, es entonces cada ̀̀twist'' de sobre una curva plana lisa sobre ?. Para ambas preguntas la respuesta es no en general. Obtenemos resultados para las cuales las preguntas anteriores siempre tienen una respuesta afirmativa, y mostramos diferentes ejemplos con respecto a la respuesta general negativa. Curiosamente, en la forma de obtener estos ejemplos, tenemos que manejar con superficies no-triviales de Brauer-Severi, y somos capaces de calcular ecuaciones explícitas de una no trivial. En tercer lugar, obtenemos una denominada clasificación representativa de los estratos por grupo de automorfismos de curvas planas no singulares sobre de género , donde es perfecto de característica o . Curiosamente, en la forma de obtener estas familias, encontramos dos fenómenos notables que no aparecieron anteriormente para género 3. Una, es la existencia de un estrato final no zero dimensional de curvas planas no-singular. Observamos en la tesis que esta es una situación usual cuando el género crece y aportamos una explicación. Describimos explícitamente familias representativas para todos los estratos, excepto para el estrato con grupo de automorfismo cíclico de orden , pero en este caso podemos demostrar la existencia de tal familia aplicando una versión del teorema de Lüroth en dimensión 2. Aquí encontramos la segunda diferencia con el caso de género inferior donde las técnicas conocidas no funcionan completamente. Por último, sea un cuerpo perfecto de característica distinta de , y sea una curva plana lisa sobre cuyo grupo de automorfismo de C sea -conjugado a un grupo diagonal. Se sabe por el trabajo de B. Huggins en su tesis doctoral (2010, Berkeley) que el cuerpo de moduli de , relativo a la extensión de Galois no necesita ser un cuerpo de definición. Motivados por estos resultados, nos preguntamos sobre las caracterizaciones de tales curvas no definibles sobre su cuerpo de moduli. Distinguimos entre los dos casos dependiendo de si el número de puntos del plano proyectivo fijados por el grupo de automorfismo es finito o infinito. Nuestros resultados pueden ser utilizados como una fuente constructiva de ejemplos para curvas planas lisas con automorfismo cíclico donde el cuerpo de moduli no es un cuerpo de definición.Smooth projective curves over a field with non-trivial automorphism group are always of deep interest in the literature. Following the philosophy of Diophantine equations theory, the simplest case is to consider smooth plane curves over of geometric genus In the thesis, we study the stratification of smooth plane curves by their automorphism groups and we deal with both algebraic and arithmetic geometry aspects. We first give a general study of the stratum, consisting of -isomorphism classes of smooth plane curves of fix genus with a fixed automorphism subgroup , where is a fixed algebraic closure of . In particular, a detailed study of the structure of their automorphism group and the associated defining equations is investigated. Second, let be a smooth projective curve defined over , which is also plane viewed as a smooth curve over . We aim to study fields of definition for non-singular plane models of and also of its twists over k by considering the embedding into instead of the one given by the canonical model into More concretely, we ask whether is a smooth plane curve over or not; and if the answer is yes, is every twist of over also a smooth plane curve over For both questions the answer is no in general, it is not. We obtain results for the curves for which the above questions always have an affirmative answer, and we show different examples concerning the negative general answer. Interestingly, in the way to get these examples, we need to handle with non-trivial Brauer-Severi surfaces, and we are able to compute explicit equations of a non-trivial one. As far as we know, this is the first time that such equations are exhibited. Third, we obtain a so-called representative classification for the strata by automorphism group of smooth -plane curves of genus , where is perfect of characteristic or . Interestingly, in the way to get these families, we find two remarkable phenomena that did not appear before. One is the existence of a non -dimensional final stratum of plane curves. At a first sight it may sound odd, but we will see that this is a normal situation for higher degrees and we will give an explanation for it. We explicitly describe representative families for all strata, except for the stratum with cyclic automorphism group of order (fortunately, we are still able to prove the existence of such family by applying a version of Lüroth's theorem in dimension 2). Here we find the second difference with the lower genus cases where the known techniques do not fully work. Finally, let be a perfect field of characteristic different from , and be a smooth plane curve over whose automorphism group of is -conjugate to a diagonal group. It is known from the work of B. Huggins in her PhD thesis (2010, Berkeley) that the field of moduli for , relative to the Galois extension does not need to be a field of definition. Motivated by these results, we wonder about characterizations of such curves not definable over their field of moduli. We distinguish between the two cases depending on whether the number of points of the projective plane fixed by the automorphism group is finite or infinite. Our results can be usede as a constructive source of so many examples of smooth plane curves with cyclic automorphism where the field of moduli is not a field of definition
Reconstrucción
No full textEn el presente porfolio se pretende, en primer lugar, mostrar la evolución personal del autor, Francesc Serrano. Como estudiante del grado de Arquitectura, mi paso por la universidad ha estado estrechamente vinculado con mi profesión; ambas con un desarrollo y aprendizaje retroalimentado.En el present portfoli es pretén, en primer lloc, mostrar l'evolució personal de l'autor, Francesc Serrano. Com a estudiant del grau d'Arquitectura, el meu pas per la universitat ha estat estretament vinculat amb la meva professió; totes dues amb un desenvolupament i aprenentatge retroalimentat.In this portfolio it is intended, first of all, to show the personal evolution of the author, Francesc Serrano. As a student of the Architecture degree, my time at the university has been closely linked to my profession; both with feedback development and learning
On the tamagawa number conjecture for hecke characters
No full textIn this paper, we prove the weak p-part of the Tamagawa number conjecture in all non-critical cases for the motives associated to Hecke characters of the form φa φ̄b where φ is the Hecke character of a CM elliptic curve E defined over an imaginary quadratic field K, under certain restrictions which originate mainly from the Iwasawa theory of imaginary quadratic fields
On Jannsen's conjecture for Hecke characters of imaginary quadratic fields
No full textWe present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1. The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois group is purely of local type. Without this regularity assumption at p, we present a review of the known situations in the critical case (Section 3) and in the non-critical case (Section 4) for these realizations. We relate the conjecture to the non-vanishing of some concrete non-critical values of the associated p-adic L-function of the Hecke character. Finally, in Section 5 we prove that the conjecture follows from a general conjecture on Iwasawa theory for almost all Tate twists
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