Vol. 14, No. 9, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The Brauer group of the moduli stack of elliptic curves

Benjamin Antieau and Lennart Meier

Vol. 14 (2020), No. 9, 2295–2333
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.

Keywords
Brauer groups, moduli of elliptic curves, level structures, Hilbert symbols
Mathematical Subject Classification 2010
Primary: 14F22
Secondary: 14H52, 14K10
Milestones
Received: 10 November 2017
Revised: 26 March 2020
Accepted: 4 May 2020
Published: 13 October 2020
Authors
Benjamin Antieau
Department of Mathematics
Northwestern University
Chicago, IL
United States
Lennart Meier
Mathematical Institut
Universiteit Utrecht
Utrecht
Netherlands