{"docId":5294,"paperId":4134,"url":"https:\/\/epiga.episciences.org\/4134","doi":"10.46298\/epiga.2019.volume3.4134","journalName":"\u00c9pijournal de G\u00e9om\u00e9trie Alg\u00e9brique","issn":"","eissn":"2491-6765","volume":[{"vid":361,"name":"Volume 3"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1702.04404","repositoryVersion":3,"repositoryLink":"https:\/\/arxiv.org\/abs\/1702.04404v3","dateSubmitted":"2017-12-11 10:11:11","dateAccepted":"2019-03-20 09:30:12","datePublished":"2019-03-20 09:34:46","titles":["$\\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$"],"authors":["Sawin, Will"],"abstracts":["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"],"keywords":["Mathematics - Algebraic Geometry","14M20"]}