摘要翻译:
Bogomolov猜想是关于定义在整体域上的光滑完全曲线上的小高度代数点的有限性陈述。对于定义在特征为零的函数域上的亏格至多为4的所有曲线,我们证明了Bogomolov猜想的一个有效形式。我们恢复了对属2曲线的已知结果,并在许多情况下改进了对属3曲线的已知界。对于许多降阶不良的亏格4曲线,该猜想以前是未证明的。
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英文标题:
《The Geometric Bogomolov Conjecture for Small Genus Curves》
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作者:
X.W.C. Faber
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
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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PDF链接:
https://arxiv.org/pdf/0803.0855