Tim Dokchitser
Published 2010-09-27, updated 2012-01-17Version 2
This is an expository article, based on a lecture course given at CRM Barcelona in December 2009. The 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 discuss some peculiar consequences of the parity conjecture.
Comments: minor corrections, to appear in a CRM Advanced Courses volume "Elliptic curves, Hilbert modular forms and Galois deformations"; 43 pages
Journal: Elliptic Curves, Hilbert Modular Forms and Galois Deformations, Advanced Courses in Mathematics - CRM Barcelona, Springer Basel, 2013
Parity conjectures for elliptic curves over global fields of positive characteristic
Canonical heights on elliptic curves in characteristic p
Park City lectures on elliptic curves over function fields
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