Cohomologie de fibrés en droite sur le fibré cotangent de variétés grassmanniennes généralisées

Cette thèse s'intéresse à la cohomologie de fibrés en droite sur le fibré cotangent de variétés projectives. Plus précisément, pour $G$ un groupe algébrique simple, connexe et simplement connexe, $P$ un sous-groupe maximal de $G$ et $\omega$ un générateur dominant du groupe de caractères de $P$, on cherche à comprendre les groupes de cohomologie $H^i(T^*(G/P),\mathcal{L})$ où $\mathcal{L}$ est le faisceau des sections d'un fibré en droite sur $T^*(G/P)$. Sous certaines conditions, nous allons montrer qu'il existe un isomorphisme, à graduation près, entre $H^i(T^*(G/P),\mathcal{L})$ et $H^i(T^*(G/P),\mathcal{L}^{\vee})$ Après avoir travaillé dans un contexte théorique, nous nous intéresserons à certains sous-groupes paraboliques en lien avec les orbites nilpotentes. Dans ce cas, l'algèbre de Lie du radical unipotent de $P$, que nous noterons \nLie, a une structure d'espace vectoriel préhomogène. Nous pourrons alors déterminer quels cas vérifient les hypothèses nécessaires à la preuve de l'isomorphisme en montrant l'existence d'un $P$-covariant $f$ dans \comp[\nLie] et en étudiant ses propriétés. Nous nous intéresserons ensuite aux singularités de la variété affine $V(f)$. Nous serons en mesure de montrer que sa normalisation est à singularités rationnelles.In this thesis, we study the cohomology of line bundles on cotangent bundle of projective varieties. To be more precise, let $G$ be an semisimple algebraic group which is simply connected, $P$ a maximal subgroup and $\omega$ a dominant weight that generates the character group of $P$. Our goal is to understand the cohomology groups $H^i(T^*(G/P),\mathcal{L})$ where $\mathcal{L}$ is the sheaf of sections of a line bundle on $T^*(G/P)$. Under some conditions, we will show that there exists an isomorphism, up to grading, between $H^i(T^*(G/P),\mathcal{L})$ and $H^i(T^*(G/P),\mathcal{L}^{\vee})$. After we worked in a theoretical setting, we will focus on maximal parabolic subgroups related to nilpotent varieties. In this case, the Lie algebra of the unipotent radical of $P$ has a structure of prehomogeneous vector spaces. We will be able to determine which cases verify the hypothesis of the isomorphism by showing the existence of a $P$-covariant $f$ in \comp[\nLie] and by studying its properties. We will be interested by the singularities of the affine variety $V(f)$. We will show that the normalisation of $V(f)$ has rational singularities

Le théorème de Borel-Weil-Bott

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Effect of interaction between Streptococcus lactis and Aspergillus flavus on the production of aflatoxin.

The inoculation of Aspergillus flavus spores into a culture of Streptococcus lactis in LTB medium resulted in none or little aflatoxin production even though growth of the fungus was not hindered. The drop in pH and reduced nutrients in the medium as the result of S. lactis growth were not the cause of the observed inhibition. The inhibition was not eliminated by the addition of carbohydrate equal to the amount utilized by the bacterium prior to the inoculation with the fungus. Aflatoxin production was also inhibited when S. lactis was inoculated after A. flavus had grown. In addition to inhibiting the synthesis of aflatoxin, S. lactis also degraded pre-formed toxin. Aflatoxin, on the other hand, not only reduced the growth of S. lactis but also affected the morphology of the bacterial cell--the cells became elongated and formed long chains.S. lactis produced and excreted the inhibitor into the medium during the early stage of growth (4 h). The inhibitor was a heat stable low molecular weight compound (MW (LESSTHEQ) 500). Neither volatile (acetic) nor non-volatile (succinic and lactic) acids which were detected in extracts containing the inhibitor were responsible for this inhibition. Lactic acid was found in larger quantities in mixed cultures and its addition to mono fungus culture was found to stimulate aflatoxin production. Chloroform: methanol extraction of the S. lactis culture filtrate removed all the activity to the organic phase. Further, the active compound was insoluble in hexane, not extracted by sodium bicarbonate and was soluble in acetone, indicating a polar lipid. Autoradiographic studies showed that the inhibitor was a product of glucose metabolism. Further characterization indicated that the inhibitor was a phosphoglycolipid containing an aromatic ring structure.Filtrate extracts of A. flavus grown in presence of S. lactis were toxic to Bacillus megaterium but did not exhibit mutagenic or carcinogenic activity in the Salmonella/Mammalian microsome mutagenicity test

Typology of incoherence due to the didactic transposition in Quebec textbooks introducing abstract algebra

International audienceAs shown in the Quebec Ministry of Education curriculum, the first notions of abstract algebra are presented in the linear algebra class, at CEGEP level (students of 17 to 19 years old). After a census of the 13 French CEGEP of Montreal region, which offer pre-university preparation for mathematics, we found out that four textbooks (regularly re-edited) are used by the majority of teachers as guidance for this class (Ouellet, 2002; Amyotte, 2009; Charron & Parent, 2005; Papillon, 1993, 2012). Unlike high schools, CEGEP are free to choose the didactic material they propose to their students; textbooks do not have to be approved by a Ministerial commission. However, for the sake of consistency, editors try to respect ministerial guidance and organise the textbooks following objectives given by the ministry. Notably, amongst those programme objectives (MELS, 2010, p. 5), we found that the most relevant to the class of linear algebra students were: — identify a certain amount of ideas in link with the subject to compare, classify and evaluate them; — link pertinent ideas in a logical order; — building a coherent argument / reasoning / proof (loose translation)

Lactic Acid Bacteria as Antifungal and Anti‐Mycotoxigenic Agents: A Comprehensive Review

Fungal contamination of food and animal feed, especially by mycotoxigenic fungi, is not only a global food quality concern for food manufacturers, but it also poses serious health concerns because of the production of a variety of mycotoxins, some of which present considerable food safety challenges. In today's mega-scale food and feed productions, which involve a number of processing steps and the use of a variety of ingredients, fungal contamination is regarded as unavoidable, even good manufacturing practices are followed. Chemical preservatives, to some extent, are successful in retarding microbial growth and achieving considerably longer shelf-life. However, the increasing demand for clean label products requires manufacturers to find natural alternatives to replace chemically derived ingredients to guarantee the clean label. Lactic acid bacteria (LAB), with the status generally recognized as safe (GRAS), are apprehended as an apt choice to be used as natural preservatives in food and animal feed to control fungal growth and subsequent mycotoxin production. LAB species produce a vast spectrum of antifungal metabolites to inhibit fungal growth; and also have the capacity to adsorb, degrade, or detoxify fungal mycotoxins including ochratoxins, aflatoxins, and Fusarium toxins. The potential of many LAB species to circumvent spoilage associated with fungi has been exploited in a variety of human food and animal feed stuff. This review provides the most recent updates on the ability of LAB to serve as antifungal and anti-mycotoxigenic agents. In addition, some recent trends of the use of LAB as biopreservative agents against fungal growth and mycotoxin production are highlighted