TY - JOUR
T1 - Non-archimedean analytification of algebraic spaces
AU - Brian, Conrad
AU - Michael, Temkin
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77951783913&partnerID=8YFLogxK
U2 - 10.1090/s1056-3911-09-00497-4
DO - 10.1090/s1056-3911-09-00497-4
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77951783913
SN - 1056-3911
VL - 18
SP - 731
EP - 788
JO - Journal of Algebraic Geometry
JF - Journal of Algebraic Geometry
IS - 4
ER -