论文标题
Galois专业至对称点和逆Galois问题最高$ s_n $
Galois specialization to symmetric points and the inverse Galois problem up to $S_n$
论文作者
论文摘要
该论文与希尔伯特（Hilbert）的不可约性定理的以下版本有关：如果$π：x \ to y $是一个galois $ g $ - 在数字字段$ k $和$ h \ subset g $上覆盖的品种是一个子组，那么所有足够大的$ n $ $ n $ $ n $ n $ y y $ y y y y y y y y y | $ k（x）/k（y）$的π^{ - 1}（y）$是agalois $ h $ extension，$ k（y）/k $是$ s_n $ extension。当应用于各种模量空间时，结果具有有趣的推论。例如，对于每个有限的$ g $，都有一个常数的$ n $，以便对于所有$ n> n $，都有$ n $，$ s_n $ extension $ f/\ mathbb {q} $，因此，$ g $的$ f $超过$ f $ for $ f $ for $ g $具有解决方案。
The paper is concerned with the following version of Hilbert's irreducibility theorem: if $π: X \to Y$ is a Galois $G$-covering of varieties over a number field $k$ and $H \subset G$ is a subgroup, then for all sufficiently large and sufficiently divisible $n$ there exist a degree $n$ closed point $y \in |Y|$ and $x \in π^{-1}(y)$ for which $k(x)/k(y)$ is a Galois $H$-extension, and $k(y)/k$ is an $S_n$-extension. The result has interesting corollaries when applied to moduli spaces of various kinds. For instance, for every finite group $G$ there is a constant $N$ such that for all $n>N$ there is a degree $n$, $S_n$-extension $F/\mathbb{Q}$ such that over $F$ the inverse Galois problem for $G$ has a solution.
