10.46298/epiga.2019.volume3.4134
https://epiga.episciences.org/4134
Sawin, Will
Will
Sawin
$\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$
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.
Comment: 10 pages, published version
episciences.org
Mathematics - Algebraic Geometry
14M20
2019-03-20
2019-03-20
2019-03-20
eng
journal article
arXiv:1702.04404
10.48550/arXiv.1702.04404
2491-6765
https://epiga.episciences.org/4134/pdf
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Épijournal de Géométrie Algébrique
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