### Parity of ranks of elliptic curves I

Dokchitser, V *(Cambridge)*

Tuesday 15 December 2009, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

I will explain why both the Birch-Swinnerton-Dyer conjecture and the Shafarevich-Tate conjecture imply that the parity of the rank of an elliptic curve over a number field can be expressed as a sum of (computable) local invariants, and describe some arithmetic consequences.

#### Video

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