Hauteurs de sous-espaces sur les corps non commutatifs

Liebendörfer, Christine and Rémond, Gaël. (2007) Hauteurs de sous-espaces sur les corps non commutatifs. Mathematische Zeitschrift, 255 (3). pp. 549-577.

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We study heights of subspaces of D N where D is a finite-dimensional rational division algebra and N a positive integer. We define them in terms of volumes of Euclidean lattices by extending a formula of W. Schmidt so that we recover the classical height if D is commutative. We review basic properties, prove a Siegel Lemma over D, a duality theorem and a new formula for the degree of certain abelian varieties. We further give matrix versions and compare our notion with the height defined through algebraic groups by J. Franke, Y. Manin and Y. Tschinkel
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Zehrt, Christine
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:16 Dec 2020 12:30
Deposited On:16 Dec 2020 12:30

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