Some properties of a Brauer class

2019/08/08 by Qixiao Ma, Ma, Qixiao
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1908.03131

openalex publication_date 2019/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth proper curve defined over a field k. The representability of the relative Picard functor is obstructed by a class α\inBr(Pic_X/k). We show the associated division algebra on Pic⁰_X/k has natural involutions. We show the class α splits at some height one points in Pic_X/k.

Related

• Brauer classes not split by genus one curves
• Brauer class over the Picard scheme of totally degenerate stable curves
• Splitting unramified Brauer classes by abelian torsors and the period-index problem
• Splitting Brauer classes by genus one curves over number fields
• Invariants of Vanishing Brauer Classes