The Birch and Swinnerton-Dyer conjecture for Q-curves
Institution: | McGill University |
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Department: | Department of Mathematics and Statistics |
Degree: | PhD |
Year: | 2011 |
Keywords: | Pure Sciences - Mathematics |
Record ID: | 1895787 |
Full text PDF: | http://digitool.library.mcgill.ca/thesisfile103574.pdf |
The main result of this thesis is the proof of a Kolyvagin-like result for Q-curves defined over Q=(square root N) of perfect square conductor (including trivial conductor) over that field. Such a setting lies beyond the scope of the general results of Zhang [Zh1] because of the absence of a Shimura curve parameterization for E. This thesis also describes an explicit construction of Heegner points on E in a setting which so far has not yet studied in the literature and provides numerical examples. In turn, these computations yield numerical evidence for a conjectural connection, which we propose in this thesis, between the Heegner points we construct and the ATR points obtained by Darmon-Logan in [DL].