论文标题
关于惯性的猜想及其概括
On the Inertia Conjecture and its generalizations
论文作者
论文摘要
在研究投影线的两个分支的Galois封面我们证明了交替组的惯性猜想和$ p \ geq 17 $。我们获得了雷诺（Raynaud）对修补结果的概括，从而减少了这些证据，以显示仿射线的oftale galois封面的实现，而惯性组的候选者却少于$ \ iftty $。我们还提出了一个由惯性猜想引起的一般问题，并获得了一些肯定的结果。这个问题的一个特殊情况，我们称为广义纯粹的野性猜想，对于已经建立了惯性猜想的纯粹野生部分的群体被证明是正确的。特别是，我们表明，如果对于没有共同商的组$ g_1 $和$ g_2 $的$ g_1 $和$ g_2 $是正确的，那么产品$ g_1 \ times g_2 $也是如此。
Studying two point branched Galois covers of the projective line we prove the Inertia Conjecture for the Alternating groups $A_{p+1}$, $A_{p+3}$, $A_{p+4}$ for any odd prime $p \equiv 2 \pmod{3}$ and for the group $A_{p+5}$ when additionally $4 \nmid (p+1)$ and $p \geq 17$. We obtain a generalization of a patching result by Raynaud which reduces these proofs to showing the realizations of the étale Galois covers of the affine line with a fewer candidates for the inertia groups above $\infty$. We also pose a general question motivated by the Inertia Conjecture and obtain some affirmative results. A special case of this question, which we call the Generalized Purely Wild Inertia Conjecture, is shown to be true for the groups for which the purely wild part of the Inertia Conjecture is already established. In particular, we show that if this generalized conjecture is true for the groups $G_1$ and $G_2$ which do not have a common quotient, then the conjecture is also true for the product $G_1 \times G_2$.
