In this paper we study the automorphism group of the procongruence mapping class group through its action on the associated procongruence curve and pants complexes. Our main result is a rigidity theorem for the procongruence completion of the pants complex. As an application we prove that moduli stacks of smooth algebraic curves satisfy a weak anabelian property in the procongruence setting.

中文翻译：

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同余曲线和裤子复合体的自同构

在本文中，我们通过其对相关同余曲线和裤子复合体的作用来研究同余映射类群的自同构群。我们的主要结果是裤子复合体同余完成的刚性定理。作为一个应用，我们证明平滑代数曲线的模叠加在同余设置下满足弱阿贝尔性质。