Approximating rational points on surfaces

Brian Lehmann; David McKinnon; Matthew Satriano

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Approximating rational points on surfaces

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arxiv 2403.02480 v1 pith:JNNX6C2K submitted 2024-03-04 math.AG math.NT

Approximating rational points on surfaces

Brian Lehmann , David McKinnon , Matthew Satriano This is my paper

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keywords conjecturerationalpointsstrategysurfacesalgebraicapproximatingapproximations

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Let $X$ be a smooth projective algebraic variety over a number field $k$ and $P$ in $X(k)$. In 2007, the second author conjectured that, in a precise sense, if rational points on $X$ are dense enough, then the best rational approximations to $P$ must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta's conjecture, and execute this strategy for the full conjecture for split surfaces.

Approximating rational points on surfaces

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