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arXiv:1010.0152 [math.NT]AbstractReferencesReviewsResources

The average rank of elliptic $n$-folds

Remke Kloosterman

Published 2010-10-01, updated 2011-02-17Version 2

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.

Comments: Expansion of the discussion of the cycle class map; several minor changes
Categories: math.NT, math.AG
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