TL;DR
This paper extends previous results on a conjecture by Colliot-Thelene, providing refined conditions for when morphisms of varieties are surjective on local points across almost all localizations.
Contribution
It offers new necessary and sufficient conditions for the surjectivity of morphisms on local points, refining earlier conjectures and results.
Findings
Provides refined criteria for surjectivity on local points
Extends previous results by Denef, Loughran, Skorobogatov, Smeets
Clarifies the conditions under which morphisms are surjective almost everywhere
Abstract
The aim of this short note is to extend results by Denef and Loughran, Skorobogatov, Smeets concerning refinements of a conjecture of Colliot-Thelene. The problem is about giving necessary and sufficient conditions for morphisms of varieties to be surjective on local points for almost all localizations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Mathematical Dynamics and Fractals