Mathematics of the USSR-Izvestiya · 1992 · 14 citations · 8 references
Natural SciencesMathematicsGeometryNumber TheoryPhilosophy Of MathematicsAbstract AlgebraAlgebraic GeometryArithmetic GeometryComplex GeometryElliptic CurvesGalois TheoryAbelian CategoriesFiniteness ConditionsFiniteness TheoremsHeegner PointsJacobian VarietiesShimura VarietiesTorsionTorsion Points On Abelian Varieties
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.
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Heegner points and derivatives ofL-series
Benedict H. Gross, Don Zagier · Inventiones mathematicae · 1986 · 972 citations
Construction of Class Fields and Zeta Functions of Algebraic Curves
Goro Shimura · Annals of Mathematics · 1967 · 171 citations