论文标题
差异Galois组，专业和Matzat的猜想
Differential Galois groups, specializations and Matzat's conjecture
论文作者
论文摘要
我们研究了由代数品种$ \ Mathcal {x} $参数参数的线性微分方程的家族，并证明所有点$ x \ in \ Mathcal {x} $的集合，使得通用光纤的差异galois组可用于$ x $ x $ x $ xariski $ x $ n c $ x $ ns $ x $ ns $ x $ ns $ x $ {作为一个应用程序，我们证明了MATZAT的猜想完全普遍性：在特征零的代数封闭字段上的一个可变性函数字段的绝对差分galois组是一个自由的proalgebraic组。
We study families of linear differential equations parametrized by an algebraic variety $\mathcal{X}$ and show that the set of all points $x\in \mathcal{X}$, such that the differential Galois group at the generic fibre specializes to the differential Galois group at the fibre over $x$, is Zariski dense in $\mathcal{X}$. As an application, we prove Matzat's conjecture in full generality: The absolute differential Galois group of a one-variable function field over an algebraically closed field of characteristic zero is a free proalgebraic group.
