代数学コロキウム

過去の記録 ~04/13次回の予定今後の予定 04/14~

開催情報 水曜日 17:00~18:00 数理科学研究科棟(駒場) 117号室
担当者 今井 直毅,ケリー シェーン

2021年10月20日(水)

17:00-18:00   オンライン開催
Alex Youcis 氏 (東京大学大学院数理科学研究科)
Geometric arc fundamental group (English)
[ 講演概要 ]
Unlike algebraic geometry, the correct notion for a ‘covering space’ of a rigid analytic variety is non-obvious to define. In particular, the class of finite etale covering spaces doesn’t encompass many real world examples of ‘covering space’-like maps (e.g. Tate’s uniformization of elliptic curves, or period mappings of Rapoport—Zink spaces). In de Jong’s seminal work on the topic he made great strides forward by studying a notion of covering space, suggested by work of Berkovich, which includes many previous ‘covering spaces’ which are not finite etale and is rich enough to support a theory of a fundamental group.

Unfortunately, de Jong’s notion of covering space lacks many of the natural properties one would expect from the notion of a ‘covering space’. In this talk we discuss recent work of Achinger, Lara, and myself which proposes a larger class of ‘covering spaces’ than those considered by de Jong which enjoys the geometric properties missing from de Jong’s picture. In addition, we mention how this larger category is related to work of Scholze on pro-etale local systems as well as work of Bhatt and Scholze on the pro-etale fundamental group of a scheme.