Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Non-archimedean analytification of algebraic spaces

Authors: Brian Conrad and Michael Temkin
Journal: J. Algebraic Geom. 18 (2009), 731-788
Published electronically: April 7, 2009
MathSciNet review: 2524597
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Abstract | References | Additional Information

Abstract: 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 separatedness hypothesis on the equivalence relation. We also give counterexamples that show the necessity of separatedness hypotheses, in contrast with the complex-analytic case. As an application, we construct analytifications for separated algebraic spaces over a non-archimedean field.

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Additional Information

Brian Conrad
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305

Michael Temkin
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Received by editor(s): June 22, 2007
Received by editor(s) in revised form: September 14, 2007
Published electronically: April 7, 2009
Additional Notes: The work of the first author was partially supported by NSF grant DMS-0600919, and both authors are grateful to the participants of the Arizona Winter School for helpful feedback on an earlier version of this paper. Also, the first author is very grateful to Columbia University for its generous hospitality during a sabbatical visit.

American Mathematical Society