TITLE: Weierstrass points on rigid-analytic surfaces
QUESTION [8 upvotes]: Does a rigid-analytic surface defined over a nonarchimedean complete field have Weierstrass points (if its genus is big enough let's say)? Is there a good reference that (ideally) lists theorems for rigid-analytic spaces that are the analog of commonly known theorems about complex analytic spaces?

REPLY [3 votes]: About references I think Brian Conrad's lecture notes (I'd check mainly his references) from his course in AWS07 might be a good place to look at. http://swc.math.arizona.edu/aws/07/ConradNotes11Mar.pdf
From Conrad's notes I remember that two references were helpful,
http://wwwmath.uni-muenster.de/sfb/about/publ/heft378.pdf
and "Non-Archimedean analysis" by S. Bosch, U. Güntzer, R. Remmert