Notes on the Parity Conjecture

Details Notes on the Parity Conjecture Notes on the Parity Conjecture

2010-09-27

arxiv.org/abs/1009.5389v2

Mathematics

Number Theory

minor corrections, to appear in a CRM Advanced Courses volume "Elliptic curves, Hilbert modular forms and Galois deformations"

Scientific paper

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.

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