Title: $\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$,
Abstract: Using etale cohomology, we define a birational invariant for varieties in
characteristic $p$ that serves as an obstruction to uniruledness - a variant on
an obstruction to unirationality due to Ekedahl. We apply this to
$\overline{M}_{1,n}$ and show that $\overline{M}_{1,n}$ is not uniruled in
characteristic $p$ as long as $n \geq p \geq 11$. To do this, we use Deligne's
description of the etale cohomology of $\overline{M}_{1,n}$ and apply the
theory of congruences between modular forms.