Rigidity of the arithmetic fundamental group of punctured projective line.
Rigidity of the arithmetic fundamental group of punctured projective line.
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穿刺射影线算术基本群的刚度。
DOI：
10.1515/crll.1990.405.117
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
Hiroaki Nakamura
中科院分区：
文献类型：
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作者：
Hiroaki Nakamura
其中E是k的固定代数闭包，G（k）是域扩张k/k的伽罗瓦群。正如Grothendieck最近的程序[6]，[7]所建议的那样，我们可以预期，在某种“anabelian”的情况下，群增广“Px/k ι W -* G（/c）”是如此严格，以至于可以确定簇X/k本身。我们说两个代数簇X/k和X '/k在k上是n^-等价的，如果存在一个profinite群同构α：π i（X）-> ni（X）使得px/k = pX'ik ° a。显然k上的k-同构簇是Ti^-等价的。我们的指导问题是找到一些条件下，逆蕴涵成立。
where £ is a fixed algebraic closure of k and G (k) is the Galois group of the field extension k/k. As suggested in the Grothendieck's recent programs [6], [7], we may expect, under a certain "anabelian" circumstance, that the group augmentation "Px/k ι W —* G(/c)" is so rigid s to determine the variety X/k itself. We shall say that two algebraic varieties X/k and X'/k are n^-equivalent over k, if there exists a profinite group isomorphism α : πί(Χ) —> ni(X) such that px/k = pX'ik ° a. Obviously /c-isomorphic varieties are Ti^-equivalent over k. Our guiding problem is to find some conditions under which the inverse implication holds.