The University of Arizona

Rational curves on elliptic surfaces

Rational curves on elliptic surfaces

Series: Algebraic Geometry Seminar
Location: ENR 2 S395
Presenter: Doug Ulmer, University of Arizona

Given a non-isotrivial elliptic curve E over K=Fq(t), there is always
a finite extension L of K which is itself a rational function field
such that E(L) has large rank.  The situation is completely different
over complex function fields: For "most" E over K=C(t), the rank E(L)
is zero for any rational function field L=C(u).  The yoga that
suggests this theorem leads to other remarkable statements about
rational curves on surfaces generalizing a conjecture of Lang.

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