The Brauer group of the moduli stack of elliptic curves

Benjamin Antieau, Lennart Meier

Published 2016-08-02Version 1

We compute the Brauer group of the moduli stack of elliptic curves over the integers and over localizations of the integers. The methods involved include the descent spectral sequence in \'etale cohomology, group cohomology calculations for S3, the classification of cubic Galois extensions of Q, the computation of Hilbert symbols in the ramified case for the primes 2 and 3, and finally finding p-adic elliptic curves with specified properties.