FINITENESS OF OVER TOTALLY REAL FIELDS

Abstract

Kolyvagin's method for the proof of the finiteness of is extended to abelian varieties with real multiplication, of -rank 0, defined over totally real fields, if they are factors of the Jacobians of Shimura curves. The finiteness of for such a variety is proved, starting from the conditions that a Heegner point on it is not a torsion point.