کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5778401 1633771 2017 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Metric uniformization of morphisms of Berkovich curves
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Metric uniformization of morphisms of Berkovich curves
چکیده انگلیسی

We show that the metric structure of morphisms f:Y→X between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton Γ=(ΓY,ΓX) of f, the sets Nf,≥n of points of Y of multiplicity at least n in the fiber are radial around ΓY with the radius changing piecewise monomially along ΓY. In this case, for any interval l=[z,y]⊂Y connecting a point z of type 1 to the skeleton, the restriction f|l gives rise to a profile piecewise monomial function φy:[0,1]→[0,1] that depends only on the type 2 point y∈ΓY. In particular, the metric structure of f is determined by Γ and the family of the profile functions {φy} with y∈ΓY(2). We prove that this family is piecewise monomial in y and naturally extends to the whole Y. In addition, we extend the classical theory of higher ramification groups to arbitrary real-valued fields and show that φy coincides with the Herbrand function of H(y)/H(f(y)). This gives a curious geometric interpretation of the Herbrand function, which also applies to non-normal and even inseparable extensions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 317, 7 September 2017, Pages 438-472
نویسندگان
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