The theory of complex multiplication has been a powerful tool for studying various aspects of classical modular forms along with their generalizations. With the recent work of Borcherds there has been an increase in the interest in studying modular forms on orthogonal groups of signature (2,n) as well as the spaces on which they live. In this thesis, we study the special points (or CM-points) that exist on these spaces. We develop cohomological classifications relating the special points, their associated CM-fields and the spaces in which these points can be found. / La théorie de la multiplication complexe nous donnent des outils puissants pour étudier des aspects divers des formes modulaires classiques, ainsi que leurs généralisations. Les travaux récents de Borcherds donne une nouvelle motivation pour étudier les formes modulaires sur des groupes orthogonaux de signature (2,n), ainsi que les espaces sur lesquels elles agissent. Dans cette thèse, nous étudierons les points spéciaux (ou points-CM) qui existent dans ces espaces. Nous développerons des classifications cohomologiques concernant les points spéciaux, les corps-CM associés et les espaces dans lesquels ces points peuvent être trouvées.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.67034 |
| Date | January 2009 |
| Creators | Fiori, Andrew |
| Contributors | Eyal Z Goren (Internal/Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics and Statistics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | Electronically-submitted theses. |
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