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arXiv · 0803.0855

The Geometric Bogomolov Conjecture for Small Genus Curves

X. W. C. Faber
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Abstract

The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the Bogomolov Conjecture for all curves of genus at most 4 defined over a function field of characteristic zero. We recover the known result for genus 2 curves and in many cases improve upon the known bound for genus 3 curves. For many curves of genus 4 with bad reduction, the conjecture was previously unproved.

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X. W. C. Faber. 2009-07-13. The Geometric Bogomolov Conjecture for Small Genus Curves. https://arxiv.org/abs/0803.0855

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