The local pro-p anabelian geometry of curves
The local pro-p anabelian geometry of curves
复制标题
曲线的局部 Pro-p 阿贝尔几何
DOI：
10.1007/s002220050381
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发表时间：
1999
影响因子：
3.1
通讯作者：
S. Mochizuki
中科院分区：
文献类型：
--
作者：
S. Mochizuki
设X是一个连通概图。然后，人们可以（在格罗滕迪克之后）将X与它的代数基本群π1（X）联系起来。这个群π1（X）是一个profinite群，它是由以下性质唯一确定的（直到内自同构）：配备有连续π1（X）-作用的有限离散集的范畴等价于X的有限根覆盖的范畴。此外，赋值X → π1（X）是从连通概型范畴（和概型的态射）到profinite拓扑群和连续外同态范畴（即，拓扑群的连续同态，其中我们识别任何两个同态，它们可以通过与内部自同构的复合而彼此获得）。
Let X be a connected scheme. Then one can associate (after Grothendieck) to X its algebraic fundamental group π1(X). This group π1(X) is a profinite group which is uniquely determined (up to inner automorphisms) by the property that the category of finite, discrete sets equipped with a continuous π1(X)-action is equivalent to the category of finite etale coverings of X. Moreover, the assignment X → π1(X) is a functor from the category of connected schemes (and morphisms of schemes) to the category of profinite topological groups and continuous outer homomorphisms (i.e., continuous homomorphisms of topological groups, where we identify any two homomorphisms that can be obtained from one another by composition with an inner automorphism).