2020/09/15 by Chang Lv, Lv, Chang · 1 citation
Mathematics · #18D30 #18F20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Primary 14G05 #secondary 18G50
paper · pdf · doi:10.48550/arxiv.2009.06915
openalex publication_date 2020/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the notion of rational points and cohomological obstructions on varieties to categories fibred in groupoids. We also establish the generalized theory of descent by torsors. Then we interpret the obstruction given by the second cohomology of abelian sheaves in terms of categorical points of gerbes, analogue to descent by torsors. As an application, we construct some composite obstructions not larger than the descent obstruction. We also propose some new kinds of obstructions including the derived obstruction, which has good behavior under a product and is also not larger than the descent obstruction.