### Arithmetic on elliptic threefolds, by Rania Wazir

In a recent paper, Rosen and Silverman showed that Tate's conjecture on
the order of vanishing of L(E,s) implies Nagao's formula, which gives the
rank of an elliptic surface in terms of a weighted average of fibral
Frobenius trace values. The aim of this paper is to extend their result to
the case of elliptic threefolds, and deduce, from Tate's conjecture, a
Nagao-type formula for the rank of an elliptic threefold E. This will
require a two-pronged approach: on the one hand, we need some
cohomological results in order to derive a Shioda-Tate formula for
elliptic threefolds; on the other, we compute an "average" number of
rational points on the singular fibers and relate this to the action of
Galois on those fibers.

Rania Wazir <rania@math.brown.edu>