标题： 算术理论的q-差分方程。 q-模拟Grothendieck-Katz关于p-曲率的猜想 显示英文标题

标题： Arithmetic theory of q-difference equations. The q-analogue of Grothendieck-Katz's conjecture on p-curvatures

摘要： 格罗滕迪克关于p-曲率的猜想预测，一个算术微分方程当且仅当其在正特征下的约化在几乎所有有限位上具有完整的有理解集时，才具有完整的代数解集。 这等价于卡茨对一般伽罗瓦群的猜想描述。 在本文中，我们证明了算术q-差分方程的一个类似陈述。 显示英文摘要

摘要： Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places. It is equivalent to Katz's conjectural description of the generic Galois group. In this paper we prove an analogous statement for arithmetic q-difference equation.