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The Brauer group of the
moduli stack of elliptic curves
Benjamin Antieau and Lennart Meier |
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Vol. 14 (2020), No. 9, 2295–2333
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Abstract |
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We compute the Brauer group of , the moduli stack of elliptic curves, over , its localizations, finite fields of odd characteristic, and algebraically closed fields of characteristic not . The methods involved include the use of the parameter space of Legendre curves and the moduli stack of curves with full (naive) level structure, the study of the Leray–Serre spectral sequence in étale cohomology and the Leray spectral sequence in fppf cohomology, the computation of the group cohomology of in a certain integral representation, the classification of cubic Galois extensions of , the computation of Hilbert symbols in the ramified case for the primes and , and finding -adic elliptic curves with specified properties. |
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Keywords
Brauer groups, moduli of elliptic curves, level structures,
Hilbert symbols
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Mathematical Subject Classification 2010
Primary: 14F22
Secondary: 14H52, 14K10
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Milestones
Received: 10 November 2017
Revised: 26 March 2020
Accepted: 4 May 2020
Published: 13 October 2020
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Authors |
| Benjamin Antieau | |
| Department of Mathematics Northwestern University Chicago, IL United States |
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| Lennart Meier | |
| Mathematical Institut Universiteit Utrecht Utrecht Netherlands |
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