Duality of Heights Over Quaternion Algebras

• Autores: Christine Liebendöfer, Gaël Rémond
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 1, 2005, págs. 61-72
• Idioma: inglés
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• Resumen

  • Given a number field K, it is well-known that the height of a subspace in KN and of its orthogonal complement coincide. We prove the analogous fact when K is replaced by a positive definite rational quaternion algebra with respect to the heights recently introduced by the first author. Since quaternion algebras are non-commutative, we cannot just follow the classical proof but have to work with localizations and certain finite rings.