论文标题
呈现最大延伸的Galois组和受限的分支
Presentations of Galois groups of maximal extensions with restricted ramification
论文作者
论文摘要
在卢博兹基（Lubotzky）的工作中，我们使用加洛伊斯（Galois）共同体来研究发电机数量和最小关系数量的差异，在Galois组$ g_s $ g_s $ g_s（k）$的最大扩展$ k $的最大扩展中，该$ k $的最大扩展是在有限的地方，$ k $ k $ a $ a $ a $ quarties $ n decies $ quartions $ q $ q $ q $ q a $ q。我们证明了全球Euler-Poincaré特征的广义版本，并为每个有限的简单$ G_S（k）$ - $ - 模块$ a $定义了$ b_s（k，a）$，以推广Koch的工作 - $ $ $ \ ell $ $ $ $ $ $ $ $ g_s（k）$ $ g_s（k）$ conecte $ g_s $ g g g_s $ g_s $ g_s $ $ g_s $。在非亚伯群岛的启发式方法的设置中，我们证明了刘-wood-wood-wood-wood-zureick-brown猜想所研究的对象总是可以通过定义中构建的随机组来实现的。
Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Galois group $G_S(k)$ of the maximal extension of a global field $k$ that is unramified outside a finite set $S$ of places, as $k$ varies among a certain family of extensions of a fixed global field $Q$. We prove a generalized version of the global Euler-Poincaré Characteristic, and define a group $B_S(k,A)$, for each finite simple $G_S(k)$-module $A$, to generalize the work of Koch about the pro-$\ell$ completion of $G_S(k)$ to study the whole group $G_S(k)$. In the setting of the nonabelian Cohen-Lenstra heuristics, we prove that the objects studied by the Liu--Wood--Zureick-Brown conjecture are always achievable by the random group that is constructed in the definition the probability measure in the conjecture.
