The average rank of elliptic $n$-folds

Abstract

Let $V/{\mathbb{F}}_q$ be a variety of dimension at least two. We show that the density of elliptic curves $E/{\mathbb{F}}_q(V)$ with positive rank is zero if $V$ has dimension at least 3 and is at most $1-{\zeta }_V(3{)}^{-1}$ if $V$ is a surface.

Expansion of the discussion of the cycle class map; several minor changes

References in corpus (2)

• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
• Arithmetic on Elliptic Threefolds