论文标题
涉及模块化$ j $功能的方程式的通用解决方案
Generic Solutions of Equations Involving the Modular $j$-function
论文作者
论文摘要
假设Schanuel的猜想和模块化Zilber-Pink猜想的模块化版本，我们表明某些涉及模块化$ J $函数的方程式的通用解决方案的存在可以减少到找到Zariski密集的解决方案集的问题。通过将某些条件施加在多样性的定义领域，我们还能够获得该结果的无条件版本。
Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain unconditional versions of this result.
