Zhang's Conjecture and the Effective Bogomolov Conjecture over function fields - Mathematics > Number TheoryReport as inadecuate




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Abstract: We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture,over a function field of characteristic 0 by proving Zhang-s Conjecture aboutcertain invariants of metrized graphs. In the function field case, theseconjectures were previously known to be true only for curves of genus at most 4and a few other special cases. We also either verify or improve the previousresults. We relate the invariants involved in Zhang-s Conjecture to the tauconstant of metrized graphs. Then we use and extend our previous results on thetau constant. By proving another Conjecture of Zhang, we obtain a new proof ofthe slope inequality for Faltings heights on moduli space of curves.



Author: Zubeyir Cinkir

Source: https://arxiv.org/







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