Non-archimedean analytification of algebraic spaces

Conrad Brian*, Temkin Michael

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study quotient problems for étale equivalence relations in non-archimedean geometry, and we construct quotients for such equivalence relations in Berkovich's category of analytic spaces, assuming a separat-edness hypothesis on the equivalence relation. We also give counterex-amples that show the necessity of separatedness hypotheses, in contrast with the complex-analytic case. As an application, we construct ana-lytifications for separated algebraic spaces over a non-archimedean field.

Original languageAmerican English
Pages (from-to)731-788
Number of pages58
JournalJournal of Algebraic Geometry
Issue number4
StatePublished - 2009
Externally publishedYes


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