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

Abstract:
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.