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The generic fibre of a fibre system of polarized abelian varieties with level structure, and with endomorphism structure coming from a CMfield, is defined over the function field of the moduli space for the abelian varieties. We prove that the points on this generic abelian variety which are defined over the function field of the moduli space form a finite group. The methods of proof generalize those of Mordell-Weil groups o¡ generic abelian varieties, Invent. Math. 81 (1985), 71-106, to whichdoi:10.2307/2046781 fatcat:wsw6inucsvbs7b7q5frgjk4pbi