2016/08/31 by Benjamin Antieau, Lennart Meier
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraically closed field #Brauer group #Cohomology #Cryptography and Residue Arithmetic #Elliptic curve #Hilbert scheme #Moduli #Moduli space #Stack (abstract data type) #Supersingular elliptic curve #math.AG #math.NT #msc:14F22 #msc:14H52 #msc:14K10 #Étale cohomology
paper · pdf · doi:10.2140/ant.2020.14.2295
published as Alg. Number Th. 14 (2020) 2295-2333 · minor corrections; to appear in Algebra & Number Theory
openalex created_date 2016/08/23 · arxiv created 2020/05/05 · openalex publication_date 2020/10/13 · arxiv updated 2020/10/21 · openalex updated_date 2026/08/05
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, 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 M(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 ℚ, the computation of Hilbert symbols in the ramified case for the primes 2 and 3, and finding p-adic elliptic curves with specified properties.