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- W1983642803 abstract "We get an analog of Kolyvagin's trace relations for a Siegel threefold X . Namely, let V ⊂ X be a Heegner curve (points of V correspond to Abelian surfaces with some fixed multiplication ring) and let T p be a Hecke correspondence on X , so T p ( V ) is a codimension 2 cycle on X . We describe the set of irreducible components of the support of T p ( V ) in terms of geometry of T p ( t ), where t ∈ X is a generic point. T p ( t ) is a three-dimensional quadric hypersurface over F p . We find also some equivalence relations on this set of irreducible components. The same method can be applied to other pairs V ⊂ X (or more generally chains X n ⊂ X n − 1 ⊂ ··· ⊂ X 1 ) of Shimura varieties, and other Hecke correspondences. Finally, we discuss the possibility of finding reductions at p of these irreducible components, and of applying the Birch–Mazur–Bloch method to prove that the Abel–Jacobi image of some linear combination of V and other similar curves is not of torsion." @default.
- W1983642803 created "2016-06-24" @default.
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- W1983642803 date "2001-02-01" @default.
- W1983642803 modified "2023-09-26" @default.
- W1983642803 title "Action of Hecke Correspondences on Heegner Curves on a Siegel Threefold" @default.
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- W1983642803 doi "https://doi.org/10.1006/jabr.2000.8490" @default.
- W1983642803 hasPublicationYear "2001" @default.
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