Approximating rational points on surfaces
arxiv(2024)
摘要
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.
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