If $k$ is a field that is complete with respect to some ultrametric valuation, then there is the "GAGR" (i.e. *géométrie algébrique et géométrie rigide*) theorem. A succinct explanation (in French, without proof) is:
<blockquote>
Jarraud, Pierre. "À propos de G. A. G. R.." Groupe de travail d'analyse ultramétrique <b>11</b> (1983-1984): 1-4.
</blockquote>
[Link][1].


  [1]: http://eudml.org/doc/91922