2021/06/27 by Jaya Nn Iyer, Iyer, Jaya, Roy Joshua⋆ +1
Mathematics · #14C25 #14D23 #14F20 #14F22 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2106.14268
openalex publication_date 2021/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the Brauer groups of algebraic stacks and GIT quotients: the only algebraic stacks we consider in this paper are quotient stacks [X/G], where X is a smooth scheme of finite type over a field k, and G is a linear algebraic group over k and acting on X, as well as various moduli stacks of principal G-bundles on a smooth projective curve X, associated to a reductive group G. We also consider the Brauer groups of the corresponding coarse moduli spaces, which most often identify with the corresponding GIT-quotients. One conclusion that we seem to draw then is that the Brauer groups (or their ℓ-primary torsion parts, for a fixed prime ℓ different from char(k)) of the corresponding stacks and coarse moduli spaces depend strongly on the Brauer group of the given scheme X.