$\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$
Keyword(s):
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
2018 ◽
Vol 51
(5)
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pp. 1179-1252
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Keyword(s):
2004 ◽
pp. 404-421
1981 ◽
pp. 127-140
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