Rational points in families of varieties
Martin Bright
TL;DR
This paper discusses the distribution and properties of rational points across families of algebraic varieties, providing insights into their arithmetic and geometric behavior.
Contribution
It offers new perspectives on rational points in families of varieties, connecting geometric structures with arithmetic properties.
Findings
Identifies conditions for the existence of rational points
Establishes bounds on the number of rational points in certain families
Provides examples illustrating the theoretical results
Abstract
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems