Modulo pp representations of reductive pp-adic groups: functorial properties

Let $F$ be a local field with residue characteristic $p$, let $C$ be an algebraically closed field of characteristic $p$, and let $\mathbf{G}$ be a connected reductive $F$-group. In a previous paper, Florian Herzig and the authors classified irreducible admissible $C$-representations of $G=\mathbf{G}(F)$ in terms of supercuspidal representations of Levi subgroups of $G$. Here, for a parabolic subgroup $P$ of $G$ with Levi subgroup $M$ and an irreducible admissible $C$-representation $\tau$ of $M$, we determine the lattice of subrepresentations of $\mathrm{Ind}_P^G \tau$ and we show that $\mathrm{Ind}_P^G \chi \tau$ is irreducible for a general unramified character $\chi$ of $M$. In the reverse direction, we compute the image by the two adjoints of $\mathrm{Ind}_P^G$ of an irreducible admissible representation $\pi$ of $G$. On the way, we prove that the right adjoint of $\mathrm{Ind}_P^G$ respects admissibility, hence coincides with Emerton's ordinary part functor $\mathrm{Ord}_{\overline{P}}^G$ on admissible representations.Comment: 39 page

Comparison of compact induction with parabolic induction

Let $F$ be any non archimedean locally compact field of residual characteristic $p$, let $G$ be any reductive connected $F$-group and let $K$ be any special parahoric subgroup of $G(F)$. We choose a parabolic $F$-subgroup $P$ of $G$ with Levi decomposition $P=MN$ in good position with respect to $K$. Let $C$ be an algebraically closed field of characteristic $p$. We choose an irreducible smooth $C$-representation $V$ of $K$. We investigate the natural intertwiner from the compact induced representation \ind_{K}^{G(F)}V to the parabolically induced representation \Ind_{P(F)}^{G(F)}(\ind_{M(F) \cap K}^{M(F)}V_{N(F)\cap K}). Under a regularity condition on $V$, we show that the intertwiner becomes an isomorphism after a localisation at a specific Hecke operator. When $F$ has characteristic 0, $G$ is $F$-split and $K$ is hyperspecial, the result was essentially proved by Herzig. We define the notion of $K$-supersingular irreducible smooth $C$-representation of $G(F)$ which extends Herzig's definition for admissible irreducible representations and we give a list of $K$-supersingular irreducible representations which are supercuspidal and conversely a list of supercuspidal representations which are $K$-supersingular.Comment: 28 page

Representations of a reductive pp-adic group in characteristic distinct from pp

We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups $G$, a list of cuspidal $C$-types $(J,\lambda)$ has been produced satisfying exhaustion, sometimes for a restricted kind of cuspidal representations, and often unicity. We verify that those lists verify Aut($C$)-stability and we produce similar lists when $C$ is no longer assumed algebraically closed. Our other main results concern supercuspidality. This notion makes sense for the representations $\lambda$ in the cuspidal $C$-types $(J,\lambda)$ as above, which involve finite reductive groups. We check that an irreducible cuspidal representation of $G$ induced from $\lambda$ is supercuspidal if and only $\lambda$ is supercuspidal.Comment: 45 pages This is the final versio

L'engagement dans les études une réalité plurielle /

"Cette recherche a été subventionnée par le Ministère de l'éducation dans le cadre du Programme d'aide à la recherche sur l'enseignement et l'apprentissage (PAREA)"Titre de l'écran-titre (visionné le 3 mai 2006)Également disponible en version papierBibliogr.: p. 70-7

Elaboration d'un guide méthodologique d'intervention lors de contamination par les salmonelles de produits laitiers au lait cru en zone de productions fromagères AOC du Massif Central

Les produits laitiers, dont les fromages au lait cru, ne sont pas les denrées alimentaires les plus fréquemment incriminées lors de toxi-infections par les salmonelles. Mais leur implication dans plusieurs épidémies communautaires ces dernières années, a obligé les filières à réagir. La filière des fromages d'Appellation d'Origine Contrôlée du Massif Central a décidé d'élaborer un guide méthodologique, présentant la démarche à appliquer dans un élevage, lors de contaminations des produits par les salmonelles. En plus d une méthodologie d'intervention précise, ce guide donne des informations de base sur ces bactéries et les dangers qu'elles représentent et fournit une liste détaillée des procédures de prélèvements susceptibles d'être réalisés durant l'investigation en élevage

The pro-region of the Kex2 endoprotease of Saccharomyces cerevisiae is removed by self-processing

AbstractWe have produced in the baculovirus/insect cells expression system a soluble secreted form of the Saccharomyces cerevisiae Kex2 endoprotease. This secreted enzyme was purified and its NH2-terminal sequence determined. The NH2-terminal sequence started at residue Leu109 of the sequence deduced from the KEX2 gene nucleotide sequence, showing that the Kex2 enzyme is produced as a proenzyme. Residue Leu109 is preceded by a pair of basic amino acid residues (Lys107-Arg108) which is a potential processing site for the Kex2 endopeptidase. Futhermore, expression of an inactive form of this truncated enzyme resulted in the production of a protein with a higher molecular weight. These observations suggest that the pro-region of Kex2 endoprotease is removed by a self-processing event