M1,n is usually not uniruled in characteristic p

Will Sawin

M_1,n is usually not uniruled in characteristic p

Research output: Contribution to journal › Article › peer-review

Abstract

Using étale 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 M_1,n and show that M_1,n is not uniruled in characteristic p as long as n ≥ p ≥ 11. To do this, we use Deligne's description of the étale cohomology of M_1,n and apply the theory of congruences between modular forms.

Original language	English (US)
Article number	29
Journal	Epijournal de Geometrie Algebrique
Volume	3
State	Published - 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

Characteristic p
Elliptic curves
Modular forms
Moduli of curves
Unirational
Uniruled
Étale cohomology

Cite this

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AB - Using étale 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 M1,n and show that M1,n is not uniruled in characteristic p as long as n ≥ p ≥ 11. To do this, we use Deligne's description of the étale cohomology of M1,n and apply the theory of congruences between modular forms.

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ER -

M_1,n is usually not uniruled in characteristic p

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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