Étale homotopy types of moduli stacks of polarised abelian schemes

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• 作者：Paola Frediani ; Frank Neumann
• 关键词：Étale homotopy theory ; Algebraic stacks ; Moduli of abelian schemes ; Principally polarised abelian varieties ; Algebraic curves
• 刊名：Journal of Homotopy and Related Structures
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：11
• 期：4
• 页码：775-801
• 全文大小：
• 刊物主题：Algebraic Topology; Algebra; Functional Analysis; Number Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1512-2891
• 卷排序：11

文摘

We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an étale homotopy point of view.