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:
Jarraud, Pierre. "À propos de G. A. G. R.." Groupe de travail d'analyse ultramétrique 11 (1983-1984): 1-4.[Link][1].