episciences.org_4134_1652741359
1652741359
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Épijournal de Géométrie Algébrique
24916765
03
20
2019
Volume 3
$\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$
Will
Sawin
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.
03
20
2019
4134
arXiv:1702.04404
10.48550/arXiv.1702.04404
https://arxiv.org/abs/1702.04404v2
https://arxiv.org/abs/1702.04404v1
10.46298/epiga.2019.volume3.4134
https://epiga.episciences.org/4134

https://epiga.episciences.org/5294/pdf