论文标题
阿贝尔计划同态同态的本地与全球原则
Local to global principles for homomorphisms of abelian schemes
论文作者
论文摘要
让$ a $ a $ b $为ABELIAN品种在功能字段$ k（s）$ k（s）$中定义的，我们建立标准，在$ s的限制图中，$ s $ k（s）$ a $ a $ b，$ b，$ b，$ b，k.我们的主要工具包括希尔伯特（Hilbertianity）方法，泰特（Tate）的猜想是由泰特（Tate），扎尔辛（Zarhin）和法丁（Faltings）证明的，以及当基本场是有限的情况下，扎尔辛（Zarhin）的微小权重猜想。
Let $A$ and $B$ be abelian varieties defined over the function field $k(S)$ of a smooth algebraic variety $S/k.$ We establish criteria, in terms of restriction maps to subvarieties of $S,$ for existence of various important classes of $k(S)$-homomorphisms from $A$ to $B,$ e.g., for existence of $k(S)$-isogenies. Our main tools consist of Hilbertianity methods, Tate conjecture as proven by Tate, Zarhin and Faltings, and of the minuscule weights conjecture of Zarhin in the case, when the base field is finite.
