AI 中文总结
本文从单阿贝尔几何角度研究混合特征局部域绝对伽罗瓦群外自同构群的有限子群，证明了存在非拟几何的有限子群，从而表明拟几何子群不能等同于所有有限子群。
AI 中文摘要
在本文中，我们从单阿贝尔几何的视角研究混合特征局部域的绝对伽罗瓦群的外自同构群的有限子群。我们将混合特征局部域的绝对伽罗瓦群的外自同构群的有限子群称为拟几何的，如果其在对应该绝对伽罗瓦群的自同构群中的逆像同构于某个混合特征局部域的绝对伽罗瓦群。众所周知，从混合特征局部域的自同构群到相关绝对伽罗瓦群的外自同构群的自然单射同态的像，给出了拟几何子群的一个典型例子。本文的主要结果断言，混合特征局部域的绝对伽罗瓦群的外自同构群存在非拟几何的有限子群。这一结果表明，混合特征局部域的绝对伽罗瓦群的外自同构群的拟几何子群集合，一般而言不能刻画为该外自同构群的所有有限子群的集合。
英文摘要
In the present paper, we study finite subgroups of the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of view of mono-anabelian geometry. We shall refer to a finite subgroup of the outer automorphism group of the absolute Galois group of a mixed-characteristic local field as quasi-geometric if its inverse image in the automorphism group of the corresponding absolute Galois group is isomorphic to the absolute Galois group of some mixed-characteristic local field. It is well-known that the image of the natural injective homomorphism from the automorphism group of a mixed-characteristic local field to the outer automorphism group of the associated absolute Galois group yields a typical example of a quasi-geometric subgroup. The main result of the present paper asserts the existence of non-quasi-geometric finite subgroups of the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields. This result shows that the set of quasi-geometric subgroups of the outer automorphism group of the absolute Galois group of a mixed-characteristic local field cannot be characterized, in general, as the set of all finite subgroups of the outer automorphism group.
