A remark on topologies for rational point sets

Oliver Lorscheid*, Cecília Salgado

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
56 Downloads (Pure)

Abstract

Let k be a ring, X be a k-scheme and R be a k-algebra endowed with an arbitrary topology. In this text, we introduce the fine topology on X(R), which is based on Grothendieck's definition of a topology for affine k-schemes. We prove that the fine topology is functorial in both X and R and that it coincides with Grothendieck's topology for affine k-schemes, with the strong topology for k-varieties over topological fields k and with the adelic topology for k-varieties over a global field k. In some concluding remarks, we explain how properties of the topology of R are reflected in geometric properties of the fine topology, and discuss a possible application to higher local fields.
Original languageEnglish
Pages (from-to)193-201
Number of pages9
JournalJournal of Number Theory
Volume159
DOIs
Publication statusPublished - Feb-2016
Externally publishedYes

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