1,720,967 research outputs found
Théorie de Hida supérieur pour le groupe unitaire GU (2,1)
No full textIn their breakthrough work, Calegari and Geraghty have shown how to bypass some serious restrictions of the original method by Taylor-Wiles, thus allowing us to attack more general modularity conjectures and related questions. Their method hinges on two conjectures, one is related to the problem of attaching Galois representations to torsion classes in the cohomology of Shimura varieties and the other to the requirement that these cohomology groups, localised at an appropriate ideal are non zero only in a certain range. The first conjecture is addressed in a great generality by Peter Scholze, but the second remains elusive. Recently, for coherent cohomology, inspired by the classical Hida theory, Vincent Pilloni has proposed a method consisting of p-adically interpolating the entire complex of coherent sheaves of automorphic forms on the Siegel threefold. This serves as a way to get around the second conjecture above and plays a crucial role in a recent work, where they show that abelian surfaces over a totally real field are potentially modular. In this thesis, we adapt the argument of Pilloni to construct a Hida complex interpolating classes in higher cohomology groups of the Picard modular surface. In a future work, we hope to use this to obtain some similar modularity results for abelian three-folds arising as Jacobians of some Picard curves.Le travaux récent de Calegari et Geraghty ont enlevé les restrictions de la méthode originale de Taylor-Wiles, cela nous permet d’attaquer les conjectures de modularité plus générales. Leur méthode se fonde sur deux autres conjectures, l'une est reliée au problème d'attacher les représentations galoisiennes aux classes de torsion dans le groupe de cohomologie de la variété de Shimura sous entendue et l'autre à la dégrée de concentration de ces groupes de cohomologie localisés. La première conjecture a été adressée dans une grande généralité par Peter Scholze mais la seconde reste évasive. Récemment, pour la cohomologie cohérente, Vincent Pilloni a développé une version de la théorie de Hida pour les groupes de cohomologie supérieurs qui construit une interpolation p-adique du complexe de cohomologie en question. Comme une application importante, nous pouvons contourner la second conjecture au dessus et en effet dans un travail commun récent, Vincent Pilloni avec ses collaborateurs ont montré que toutes les variétés abéliennes sur un corps totalement réel est potentiellement modulaire. Dans cette thèse, nous adaptons l'argument de Vincent Pilloni pour construire un complexe qui interpole les classes de cohomologie supérieurs de la variété de Picard. Ces résultats servent comme le premier pas vers la modularité potentielle des variétés abéliennes de dimension 3 qui proviennent des Jacobiens de la courbe de Picard
Théorie de Hida supérieur pour le groupe unitaire GU (2,1)
No full textIn their breakthrough work, Calegari and Geraghty have shown how to bypass some serious restrictions of the original method by Taylor-Wiles, thus allowing us to attack more general modularity conjectures and related questions. Their method hinges on two conjectures, one is related to the problem of attaching Galois representations to torsion classes in the cohomology of Shimura varieties and the other to the requirement that these cohomology groups, localised at an appropriate ideal are non zero only in a certain range. The first conjecture is addressed in a great generality by Peter Scholze, but the second remains elusive. Recently, for coherent cohomology, inspired by the classical Hida theory, Vincent Pilloni has proposed a method consisting of p-adically interpolating the entire complex of coherent sheaves of automorphic forms on the Siegel threefold. This serves as a way to get around the second conjecture above and plays a crucial role in a recent work, where they show that abelian surfaces over a totally real field are potentially modular. In this thesis, we adapt the argument of Pilloni to construct a Hida complex interpolating classes in higher cohomology groups of the Picard modular surface. In a future work, we hope to use this to obtain some similar modularity results for abelian three-folds arising as Jacobians of some Picard curves.Le travaux récent de Calegari et Geraghty ont enlevé les restrictions de la méthode originale de Taylor-Wiles, cela nous permet d’attaquer les conjectures de modularité plus générales. Leur méthode se fonde sur deux autres conjectures, l'une est reliée au problème d'attacher les représentations galoisiennes aux classes de torsion dans le groupe de cohomologie de la variété de Shimura sous entendue et l'autre à la dégrée de concentration de ces groupes de cohomologie localisés. La première conjecture a été adressée dans une grande généralité par Peter Scholze mais la seconde reste évasive. Récemment, pour la cohomologie cohérente, Vincent Pilloni a développé une version de la théorie de Hida pour les groupes de cohomologie supérieurs qui construit une interpolation p-adique du complexe de cohomologie en question. Comme une application importante, nous pouvons contourner la second conjecture au dessus et en effet dans un travail commun récent, Vincent Pilloni avec ses collaborateurs ont montré que toutes les variétés abéliennes sur un corps totalement réel est potentiellement modulaire. Dans cette thèse, nous adaptons l'argument de Vincent Pilloni pour construire un complexe qui interpole les classes de cohomologie supérieurs de la variété de Picard. Ces résultats servent comme le premier pas vers la modularité potentielle des variétés abéliennes de dimension 3 qui proviennent des Jacobiens de la courbe de Picard
Modularity theorems for abelian surfaces
No full textThis is a brief account of my results with George Boxer, Frank Calegari and Vincent Pilloni on the (potential) modularity of abelian surfaces
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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