论文标题
$ j $功能的差分存在闭合度
Differential Existential Closedness for the $j$-function
论文作者
论文摘要
我们证明了$ j $功能及其衍生物的微分方程的存在闭合猜想。它指出，在差异封闭的字段中，涉及$ j $功能的微分方程的某些方程式具有解决方案。它的后果包括对差异闭合场的$ j $ reducts的完整公理化，这是这些还原中强度最小的二分法结果，以及具有衍生物指标的模块化Zilber-Pink的功能模拟。
We prove the Existential Closedness conjecture for the differential equation of the $j$-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the $j$-function have solutions. Its consequences include a complete axiomatisation of $j$-reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.
