WEEKLY ACTIVITIES

Berkovich spaces over Z and convergent arithmetic power series
Báo cáo viên: Jérôme Poineau (Université de Caen)

Thời gian: 9h30, Thứ 6, ngày 22 tháng 11 năm 2019
Địa điểm: Hội trường Tầng 2, Nhà A6, Viện Toán học, 18 Hoàng Quốc Việt, Cầu Giấy, Hà Nội
Tóm tắt: Although Berkovich spaces usually appear in a non-archimedean setting, their general definition actually allows arbitrary Banach rings as base rings, e.g. Z endowed with the usual absolute value. Over the latter, Berkovich spaces look like fibrations that contain complex analytic spaces as well as p-adic analytic spaces for every prime number p. The global functions on those spaces are typically convergent arithmetic power series, i.e. power series with coefficients in Z with a positive radius of convergence. We will explain how the geometric setting can help prove nice properties of rings of convergent arithmetic power series such as noetherianity in
several variables, thus extending a result of D. Harbater in one variable.

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