Functiones et Approximatio Commentarii Mathematici

The Picard groups of the stacks $\mathscr{Y}_0(2)$ and $\mathscr{Y}_0(3)$

Andrew Niles

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We compute the Picard group of the stack of elliptic curves equipped with a cyclic subgroup of order two, and of the stack of elliptic curves equipped with a cyclic subgroup of order three, over any base scheme on which $6$ is invertible. This generalizes a result of Fulton-Olsson, who computed the Picard group of the stack of elliptic curves (with no level structure) over a~wide variety of base schemes.

Article information

Funct. Approx. Comment. Math. Volume 55, Number 1 (2016), 105-112.

First available in Project Euclid: 19 September 2016

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Mathematical Reviews number (MathSciNet)

Primary: 14D22: Fine and coarse moduli spaces
Secondary: 14D23: Stacks and moduli problems 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)

stacks elliptic curves Picard group moduli spaces


Niles, Andrew. The Picard groups of the stacks $\mathscr{Y}_0(2)$ and $\mathscr{Y}_0(3)$. Funct. Approx. Comment. Math. 55 (2016), no. 1, 105--112. doi:10.7169/facm/2016.55.1.7.

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