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arXiv · 2311.18132

The Brauer Group of $\mathscr{Y}_0(2)$

Niven Achenjang·Deewang Bhamidipati·Aashraya Jha·Caleb Ji·Rose Lopez
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Abstract

We determine the Brauer group of the Deligne-Mumford stack $\mathscr{Y}_0(2)$, the moduli space of elliptic curves with a marked $2$-torsion subgroup over bases of arithmetic interest. Antieau and Meier determine the Brauer group for $\mathscr{M}_{1,1}$, the moduli stack of elliptic curves by exploiting the fact it is covered by the Legendre family and using the Hochschild-Serre spectral sequence. Over an algebraically closed field, Shin uses the coarse space map to determine the Brauer group of $\mathscr{M}_{1,1}$. We combine techniques from both papers to determine the Brauer group of $\mathscr{Y}_0(2)$.

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Niven Achenjang, Deewang Bhamidipati, Aashraya Jha, Caleb Ji, Rose Lopez. 2023-11-29. The Brauer Group of $\mathscr{Y}_0(2)$. https://doi.org/10.46298/epiga.2026.13916

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