Smoothness and Classicality on eigenvarieties

Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of "classical weight" and that its Galois representation is crystalline at places dividing p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimension by making crucial use of the "patched eigenvariety"

A local model for the trianguline variety and applications

We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic varieties related to Grothendieck's simultaneous resolution of singularities. We derive several local consequences at these points for the trianguline variety: local irreducibility, description of all local companion points in the crystalline case, combinatorial description of the completed local rings of the fiber over the weight map, etc. Combined with the patched Hecke eigenvariety (under the usual Taylor-Wiles assumptions), these results in turn have several global consequences: classicality of crystalline strictly dominant points on global Hecke eigenvarieties, existence of all expected companion constituents in the completed cohomology, existence of singularities on global Hecke eigenvarieties

Une interpr\'etation modulaire de la vari\'et\'e trianguline

Using a patching module constructed in recent work of Caraiani, Emerton, Gee, Geraghty, Pa{\v{s}}k{\=u}nas and Shin we construct some kind of analogue of an eigenvariety. We can show that this patched eigenvariety agrees with a union of irreducible components of a space of trianguline Galois representations. Building on this we discuss the relation with the modularity conjectures for the crystalline case, a conjecture of Breuil on the locally analytic socle of representations occurring in completed cohomology and with a conjecture of Bella\"iche and Chenevier on the complete local ring at certain points of eigenvarieties.Comment: in Frenc

Urinary peptidomics provides a noninvasive humanized readout of diabetic nephropathy in mice

Nephropathy is among the most frequent complications of diabetes and the leading cause of end-stage renal disease. Despite the success of novel drugs in animal models, the majority of the subsequent clinical trials employing those drugs targeting diabetic nephropathy failed. This lack of translational value may in part be due to an inadequate comparability of human disease and animal models that often capture only a few aspects of disease. Here we overcome this limitation by developing a multimolecular noninvasive humanized readout of diabetic nephropathy based on urinary peptidomics. The disease-modified urinary peptides of 2 type 2 diabetic nephropathy mouse models were identified and compared with previously validated urinary peptide markers of diabetic nephropathy in humans to generate a classifier composed of 21 ortholog peptides. This classifier predicted the response to disease and treatment with inhibitors of the renin-angiotensin system in mice. The humanized classifier was significantly correlated with glomerular lesions. Using a human type 2 diabetic validation cohort of 207 patients, the classifier also distinguished between patients with and without diabetic nephropathy, and their response to renin-angiotensin system inhibition. Thus, a combination of multiple molecular features common to both human and murine disease could provide a significant change in translational drug discovery research in type 2 diabetic nephropathy

Distribution of red-spotted grouper nervous necrosis virus (RGNNV) antigens in nervous and non-nervous organs of European seabass (Dicentrarchus labrax) during the course of an experimental challenge

The distribution of red-spotted grouper nervous necrosis virus (RGNNV) antigens was examined by immunohistochemistry in the nervous and non-nervous organs of juvenile European seabass (Dicentrarchus labrax) during the course of an intramuscular infection. Histological changes resulting from the infection were evaluated from 3 days to 2 months post-infection. The specific antibody response was also studied 2 months post-challenge. Viral proteins were present throughout the experimental period in the retina (inner nuclear layer, ganglion layer, outer limiting membrane, and outer plexiform layer), brain (cerebellum and tectum opticum), and liver (hepatocytes and endothelial cells). These proteins were also observed in the renal tubular cells, white pulp of spleen, and in fibroblasts and cartilage of caudal fin. This is the first report of RGNNV proteins appearing in these organs, where the immunostaining was only detected at certain sampling times after the onset of mortality. Brain and retina of virus-exposed fish showed high levels of vacuolation, while accumulation of fat vacuoles was observed in the liver. RGNNV infection also induced a specific antibody response as measured by an ELISA. In summary, this is the first study demonstrating the presence of viral proteins in cells of caudal fin, kidney and spleen of European seabass

Programme de Langlands p-adique, invariants £ et catégories dérivées

Les résultats de cette thèse s'inscrivent dans le cadre du programme de Langlands p-adique. Lorsque V est une représentation p-adique de dimension 2 du groupe de Galois de Qp, on sait lui associer une représentation p-adique continue B(V) de GL_2(Qp). Dans un premier chapitre, nous considérons le cas où V est semi-stable non cristalline et construisons un foncteur qui, appliqué à une sous-représentation localement analytique Sigma(V) de B(V) construite par Breuil, donne le module de Fontaine de V. Cette méthode, inspirée des travaux de Carayol et Dat dans le cadre l-adique, utilise le complexe de de Rham du demi-plan de Drinfel'd. Lorsque L est une extension finie de Qp, nous étendons cette construction à certaines familles de représentations semi-stables non cristallines de dimension 2 du groupe de Galois de L, paramétrées par un [L:Qp]-uplet d'éléments du corps des coefficients. Nous proposons alors, par analogie avec les constructions de Breuil dans le cas L=Qp, la construction d'une représentation localement analytique de GL_2(L) associée à V et montrons qu'elle permet de retrouver le module de Fontaine de V par le foncteur décrit précédemment. Dans un deuxième chapitre, nous nous intéressons à certaines familles de représentations semi-stables de dimension 3 de G_Qp. Dans ce cas, la situation devient plus compliquée et nous construisons, pour toute représentation V de cette famille, non pas une représentation mais un complexe Sigma(V) de représentations localement analytiques de GL_3(Qp). Nous montrons alors qu'un analogue du foncteur du chapitre 1, mais utilisant l'espace de Drinfel'd de dimension 2, associe à Sigma(V) le module de Fontaine de V.The results of this thesis have for background the p-adic Langlands program. When V is a two dimensional p-adic representation of the Galois group of Qp, we know how to associate to V a continuous p-adic representation of GL_2(Qp). In a first chapter, we consider the case where V is semi-stable non crystalline and construct a functor which gives the Fontaine module of V, when it is applied to a locally analytic subrepresentation Sigma(V) of B(V) which was constructed by Breuil. This method, which is inspired by works of Carayol and Dat in the l-adic setting, uses the de Rham complex of Drinfel d s Half space. When L is a finite extension of Qp, we extend this construction to some families of semi-stable non crystalline two dimensional representations of G_Qp parametrized by [L:Qp]-uples of elements of the coefficient field. We propose, in analogy with Breuil s constructions, a locally analytic representation of GL_2(L) associated to V and show that we can retrieve the Fontaine module of V by the precedent functor. In a second chapter, we are intersesting by some families of semi-stable three dimensional representations of G_Qp. In this case, the situation is much more complicated and we construct, for such a representation V, not a representation but a complex Sigma(V) of locally analytic representations of GL_3(Qp). Then we show that an analog of the functor of the first chapter, but using the two dimensional Drinfel d s space, associates to Sigma(V) the Fontaine module of V.ORSAY-PARIS 11-BU Sciences (914712101) / SudocPARIS-ENS Math-Info (751052318) / SudocSudocFranceF

Smoothness and Classicality on eigenvarieties

International audienceLet p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of "classical weight" and that its Galois representation is crystalline at places dividing p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimension by making crucial use of the "patched eigenvariety"