绝对伽罗瓦群的拓扑实现
Topological realisations of absolute Galois groups
摘要：
设$F$是包含所有单位根的特征$0$域。构造了一个函子紧T2空间$X_F$，它的前有限基本群与$F$的绝对伽罗瓦群一致，即$X_F$的有限覆盖空间范畴等价于$F$的有限扩张范畴.该构造基于$F$的有理Witt向量环。在$\mathbb{Q}$的分圆扩张的情况下，$X_F$的经典基本群是$F$的绝对伽罗瓦群的（真）稠密子群。我们还讨论了这种结构的一个变体时，该领域是不需要包含所有的根的单位，在这种情况下，有自然的Frobenius型自同构编码下降沿分圆扩展。
英文摘要：
Let $F$ be a field of characteristic $0$ containing all roots of unity. We construct a functorial compact Hausdorff space $X_F$ whose profinite fundamental group agrees with the absolute Galois group of $F$, i.e. the category of finite covering spaces of $X_F$ is equivalent to the category of finite extensions of $F$. The construction is based on the ring of rational Witt vectors of $F$. In the case of the cyclotomic extension of $\mathbb{Q}$, the classical fundamental group of $X_F$ is a (proper) dense subgroup of the absolute Galois group of $F$. We also discuss a variant of this construction when the field is not required to contain all roots of unity, in which case there are natural Frobenius-type automorphisms which encode the descent along the cyclotomic extension.
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