Effectivity of Brauer-Manin obstructions on surfaces
Andrew Kresch, Yuri Tschinkel
TL;DR
This paper investigates how Brauer-Manin obstructions influence the failure of the Hasse principle and weak approximation on algebraic surfaces over number fields, providing insights into their effectiveness.
Contribution
It offers new analysis on the role of Brauer-Manin obstructions in rational points on algebraic surfaces, expanding understanding of their impact.
Findings
Brauer-Manin obstructions can explain failures of the Hasse principle.
Effectiveness varies depending on surface types.
Provides criteria for when obstructions are the only cause.
Abstract
We study Brauer-Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry