Riv.Mat.Univ.Parma (7) 3* (2004)


Prodromes for a theory of heights on non-commutative separable K-algebras

Pages: 333-345
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.

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