SMS scnews item created by Bill Unger at Mon 20 Sep 2010 1025
Type: Seminar
Distribution: World
Expiry: 23 Sep 2010
Calendar1: 23 Sep 2010 1505-1600
CalLoc1: Carslaw 535A

Computational Algebra Seminar: Dokchitser -- Ranks of elliptic curves: parity phenomena

Speaker:  Vladimir Dokchitser (Cambridge)
Title: Ranks of elliptic curves: parity phenomena
Time & Place: 3-4pm, Thursday 23 September, Carslaw 535

It is in general very difficult to compute ranks of elliptic curves over
number fields, even if equipped with any conjectures that are available. On
the other hand, the parity of the rank is (conjecturally) very easy to
determine --- it is given as a sum of purely local terms, which have a
reasonably simple classification. Since "odd rank" implies "non-zero rank"
implies "the curve has infinitely many points", this leads to a number of
(conjectural!) arithmetic phenomena.

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