前同余曲线与裤子复合体的自同构

Pub Date : 2023-07-19 DOI:10.1112/topo.12306

Marco Boggi, Louis Funar

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引用次数: 2

摘要

本文通过其在相关的普协曲线和裤子复形上的作用，研究了普协映射类群的自同构群。我们的主要结果是关于裤子复形的过程完备的一个刚性定理。作为一个应用，我们证明了光滑代数曲线的模栈在procongruence设置中满足弱的anabelian性质。

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Automorphisms of procongruence curve and pants complexes

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.

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