The topology on Berkovich affine lines over complete valuation rings
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AbstractIn this article, we give a full description of the topology of the one-dimensional affine analytic space A
1R over a complete valuation ring R (that is, a valuation ring with ‘real valued valuation’ which is complete under the induced metric), when its field of fractions K is algebraically closed. In particular, we show that A1R is both connected and locally path connected. Furthermore, A1R is the completion of K×(1,∞) under a canonical uniform structure. As an application, we describe the Berkovich spectrum M(Zp[G]) of the Banach group ring Zp[G] of a cyclic p-group G over the ring Zp of p-adic integers.
Acceptance Date12/03/2017
All Author(s) ListChi-Wai Leung, Chi-Keung Ng
Journal nameQuarterly Journal of Mathematics
Volume Number68
Issue Number4
Pages1163 - 1180
LanguagesEnglish-United States

Last updated on 2021-17-01 at 01:22