Geodesic
Finiteness of {\it Ш\/} over totally real fields
Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 829-853

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Kolyvagin's method for the proof of the finiteness of Ш is extended to abelian varieties with real multiplication, of $L$-rank 0, defined over totally real fields, if they are factors of the Jacobians of Shimura curves. The finiteness of Ш for such a variety is proved, starting from the conditions that a Heegner point on it is not a torsion point. 
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     author = {V. A. Kolyvagin and D. Yu. Logachev},
     title = {Finiteness of {\it {{\CYRSH}\/}} over totally real fields},
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V. A. Kolyvagin; D. Yu. Logachev. Finiteness of {\it Ш\/} over totally real fields. Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 829-853. http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a6/