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2020 The Brauer group of the moduli stack of elliptic curves
Benjamin Antieau, Lennart Meier
Algebra Number Theory 14(9): 2295-2333 (2020). DOI: 10.2140/ant.2020.14.2295

Abstract

We compute the Brauer group of 1,1, the moduli stack of elliptic curves, over Spec, its localizations, finite fields of odd characteristic, and algebraically closed fields of characteristic not 2. The methods involved include the use of the parameter space of Legendre curves and the moduli stack (2) of curves with full (naive) level 2 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 S3 in a certain integral representation, the classification of cubic Galois extensions of , the computation of Hilbert symbols in the ramified case for the primes 2 and 3, and finding p-adic elliptic curves with specified properties.

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Benjamin Antieau. Lennart Meier. "The Brauer group of the moduli stack of elliptic curves." Algebra Number Theory 14 (9) 2295 - 2333, 2020. https://doi.org/10.2140/ant.2020.14.2295

Information

Received: 10 November 2017; Revised: 26 March 2020; Accepted: 4 May 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172709
Digital Object Identifier: 10.2140/ant.2020.14.2295

Subjects:
Primary: 14F22
Secondary: 14H52, 14K10

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 9 • 2020
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