Non-archimedean analytification of algebraic spaces
| dc.creator | Conrad, Brian | |
| dc.creator | Temkin, Michael | |
| dc.date | 2007-06-25 | |
| dc.date.accessioned | 2026-07-07T08:12:04Z | |
| dc.date.available | 2026-07-07T08:12:04Z | |
| dc.description | It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct a quotient for any etale non-archimedean analytic equivalence relation whose diagonal is a closed immersion, and deduce that any separated algebraic space locally of finite type over any non-archimedean field $k$ is analytifiable in both the category of rigid spaces and the category of analytic spaces over $k$. Also, though local separatedness remains a necessary condition for analytifiability in either of these categories, we present many surprising examples of non-analytifiable locally separated smooth algebraic spaces over $k$ that can even be defined over the prime field. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0706.3441 | |
| dc.identifier | http://arxiv.org/abs/0706.3441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132328 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Non-archimedean analytification of algebraic spaces | |
| dc.type | text |