2022/10/31 by Tim Santens, Santens, Tim · 2 citations
Arts and Humanities · Mathematics · #11G30 #14A20 #14G12 (Primary) #14G25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2210.17184
openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This includes all stacky curves of genus g = (1)/(2), thus explaining a recent counterexample to the Hasse principle of Bhargava-Poonen. We will furthermore show that the elementary obstruction is the only obstruction to the integral Hasse principle for smooth proper integral models of stacky curves of genus g < 1. We then compute the Brauer-Manin obstruction for smooth proper integral models of stacky curves of genus (1)/(2).