Approximation theorems for classifying stacks over number fields

2025/07/18 by Ajneet Dhillon, Dhillon, Ajneet · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Tensor decomposition and applications #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2507.13900

Abstract

Approximation theorems for algebraic stacks over a number field k are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying stack BG. This result answers a very concrete question, given G-torsors P_v over k_v, where v ranges over a finite number of places, when can you approximate the P_v by a G-torsor P defined over k.

Citations

• On the Motivic Homotopy Type of Algebraic Stacks (with an appendix joint with Jack Hall)
• A Topology on Points on Stacks
• The bigger Brauer group and twisted sheaves
• Brauer groups and quotient stacks
• Derived 𝑙-adic categories for algebraic stacks

Cited by

• The étale Brauer-Manin obstruction for classifying stacks

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