Will Sawin - $\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$

epiga:4134 - Épijournal de Géométrie Algébrique, 20 mars 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.4134
$\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$Article

Auteurs : 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.


    Volume : Volume 3
    Publié le : 20 mars 2019
    Accepté le : 24 janvier 2019
    Soumis le : 11 décembre 2017
    Mots-clés : Mathematics - Algebraic Geometry,14M20
    Financement :
      Source : OpenAIRE Graph
    • Mathematical Sciences Research Institute (MSRI); Financeur: National Science Foundation; Code: 1440140

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