The Brauer Group of $\mathscr{Y}_0(2)$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914190292156416 |
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| author | Achenjang, Niven Bhamidipati, Deewang Jha, Aashraya Ji, Caleb Lopez, Rose |
| author_facet | Achenjang, Niven Bhamidipati, Deewang Jha, Aashraya Ji, Caleb Lopez, Rose |
| contents | 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 $\mathscr{Y}_0(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18132 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Brauer Group of $\mathscr{Y}_0(2)$ Achenjang, Niven Bhamidipati, Deewang Jha, Aashraya Ji, Caleb Lopez, Rose Algebraic Geometry Number Theory 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 $\mathscr{Y}_0(2)$. |
| title | The Brauer Group of $\mathscr{Y}_0(2)$ |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2311.18132 |