The Geometric Bogomolov Conjecture for Small Genus Curves

Details The Geometric Bogomolov Conjecture for Small Genus Curves The Geometric Bogomolov Conjecture for Small Genus Curves

2008-03-06

arxiv.org/abs/0803.0855v3

Experimental Mathematics, Vol. 18 (2009), No. 3, 347-367

Mathematics

Number Theory

47 pages total (31 pages in body of article, 8 pages of Mathematica code, 8 pages of Mathematica notebooks); ramification typo

Scientific paper

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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