有限生成域上仿射双曲曲线的几何m步可解Grothendieck猜想
The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields
AI总结：
本文在非交换几何中针对素域上有限生成域上的仿射双曲曲线，通过先证有限域情形、再证Oda-Tamagawa准则的几何m步可解版本，最终证明了（弱与强双非交换的）几何m步可解Grothendieck猜想。
摘要：
本文给出了非交换几何中几何m步可解Grothendieck猜想的若干新结果。具体而言，我们证明了素域上有限生成域上仿射双曲曲线的（弱双非交换和强双非交换）几何m步可解Grothendieck猜想。首先，我们证明了有限域上的该猜想；其次，证明了双曲曲线Oda-Tamagawa良好约化准则的几何m步可解版本；最后，利用这两个结果证明了素域上有限生成域上的该猜想。
英文摘要：
In this paper, we present some new results on the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bi-anabelian and strong bi-anabelian) geometrically m-step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically m-step solvable version of the Oda-Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field.
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