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In this chapter, xa explain how Grothendieck proves the existence of the Teichmüller moduli space of algebraic curves of genus g. He formulates the problem in terms of representation of a functor and he constructs the solution with the tools of algebraic geometry. He need for that new foundations of the theory of analytic spaces.

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Grothendieck and Teichmüller Modular Spaces

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  • 发表日期：

    2025年

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  • Christian Houzel

摘要

In this chapter, xa explain how Grothendieck proves the existence of the Teichmüller moduli space of algebraic curves of genus g. He formulates the problem in terms of representation of a functor and he constructs the solution with the tools of algebraic geometry. He need for that new foundations of the theory of analytic spaces.