Abstract
The main purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate–Shafarevich group implies the parity conjecture for elliptic curves over number fields. Along the way, we review local and global root numbers of elliptic curves and their classification, and we end by discussing some peculiar consequences of the parity conjecture.
The author is supported by a Royal Society University Research Fellowship.
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© 2013 Springer Basel
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Dokchitser, T. (2013). Notes on the Parity Conjecture. In: Elliptic Curves, Hilbert Modular Forms and Galois Deformations. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0618-3_5
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DOI: https://doi.org/10.1007/978-3-0348-0618-3_5
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Publisher Name: Birkhäuser, Basel
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