Research uncovers the Brauer group in the moduli space of elliptic curves with 2-torsion subgroups, highlighting key mathematical techniques.
We determine the Brauer group of the Deligne-Mumford stack Y₀(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 M1,1, 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 M1,1. We combine techniques from both papers to determine the Brauer group of Y₀(2). Comments welcome, 40 pages
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Achenjang et al. (2026) studied this question.
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