Prodromes for a theory of heights on non-commutative separable K-algebras
Received: 2 March 2004 Revised: 2 November 2004
Mathematics Subject Classification (2000): 11G50 - 12A80
Research partially supported by G.N.S.G.A of Istituto Nazionale di Alta Matematica, cofin 2002 GVA project and GTEM European training and research network
Abstract: Le K be a number field. Based on our previous result on the construction of canonical heights on separable commutative finite dimensional K-algebras we propose a definition for the canonical height on non-commutative, finite dimensional, separable K-algebras. We prove that it satisfies an averaging property analogous to the one satisfied by the Nèron-Tate height on abelian varieties and that is invariant under the group of K-algebra automorphisms of A.