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Topology on rational points over \(n\)-local fields. (English) Zbl 1361.12005

Summary: We extend Weil’s construction of topologies on sets of rational points of schemes over local fields to the case of \(n\)-local fields and their rings of integers by using the sequential properties of higher topologies. In order to do this, we endow each scheme of finite type over a sequential ring with a topology in a functorial way, and study the properties of this construction. Finally, we show openness of reduction maps for schemes of finite type over rings of integers of 2-local fields.

MSC:

12J10 Valued fields
54D55 Sequential spaces
14A15 Schemes and morphisms
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