Iterated descent obstructions for algebraic stacks

2024/09/30 by H. X. Wu, Wu, Han, Chang Lv +1 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2409.20068

openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Base on a conjecture, we prove that for any smooth separated stack of finite type over a number field, its descent obstruction equals its iterated descent obstruction. As a consequence, we show that for any algebraic stack over a number field that has a finite etale covering of a smooth geometrically integral variety, its descent obstruction equals its iterated descent obstruction.

Cited by

• Comparing local-global obstructions on algebraic stacks

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• Descent for algebraic stacks
• Descent theory for open varieties
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• The Brauer-Manin obstruction on algebraic stacks
• The étale Brauer-Manin obstruction for classifying stacks