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タイトル	A pro-algebraic fundamental group for topological spaces and an arithmetic application.
開催日時	2024年3月15日（金）16:00 - 17:00
主催者
講演者	Christopher Deninger氏 (University of Münster)
場所	慶應義塾大学理工学部（矢上キャンパス） 14棟631室 ※ 対面のみによる開催となります. ※ 講演後にDeningerさんと食事に行く予定です. 参加を希望される方は, 2月29日(木)までに dainobu@keio.jp (台信) へご連絡下さい.
内容	Using the Tannakian formalism we define and study a pro-algebraic fundamental group for connected topological spaces. Using ideas of Nori and a result of Deligne on fibre functors of Tannakian categories we also define a pseudo-torsor under this fundamental group which can serve as a replacement for the universal covering space in this generality. The group of connected components of the pro-algebraic fundamental group is the pro-étale fundamental group used by Kucharczyk and Scholze to exhibit the absolute Galois group of a field K containing all roots of unity as the fundamental group of an ordinary topological space Y_K. We calculate the pro-algebraic fundamental group of Y_K and show that Y_K also carries some information about the motivic Galois group of K. We also mention a categorial criterion derived from the work of Coulembier for the Tannakian dual of a neutral Tannaka category over a perfect field to be reduced. Part of this work is joint with Michael Wibmer.
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