曲线算术模空间上的微积分  

Calculus on arithmetic moduli of curves

作　　者：张寿武 Shouwu Zhang

机构地区：[1]Department of Mathematics,Princeton University,Princeton,NJ 08544,USA

出　　处：《中国科学：数学》2024年第12期2059-2068,共10页Scientia Sinica：Mathematica

摘　　要：本文通过Abel-Jacobi映射、Poincaré单值化和Mumford稳定投影嵌入给出曲线模空间上的度量化线丛的三种构造.我们还描述了两个算术应用:一个是袁新意关于一致Bogomolov猜想的应用,另一个是我们与高紫阳合作关于Gross-Shoen闭链和Ceresa闭链的Northcott性质的应用.We survey three constructions of metrized line bundles on the moduli of curves by means of Abel-Jacobi maps,uniformizations,and projective embeddings.We also describe two arithmetic applications:one to the uniform Bogomolov conjecture by Xinyi Yuan and the other to the Northcott property for Gross-Schoen cycles and Ceresa cycles.

关 键 词：Arakelov度量 Poincaré度量 adelic度量 

分 类 号：O186[理学—数学]