Reference for analytification of schemes/varieties It seems that algebraic geometers form some of their intuition by thinking about the analytification of a scheme. E.g. Alex Youcis mentions that this is often the "correct" topology to think about or for elliptic curves it seems indispensable to switch between the algebraic scheme and the corresponding analytified Riemann surface.
Yet, many of the introductory books like Hartshorne, Liu, Görtz do not discuss this topic (and Vakil only in very few starred exercises).
Hence my request: What's a good reference to start learning about analytifications of schemes/varieties?
 A: Since Serre's GAGA is already listed, let me add the book "Algebraic and Analytic Geometry" by Neeman. The book starts very gently (even redefines schemes etc.) and has full chapters on the analytic topology, analytification, algebraic and analytic coherent sheaves etc. so that one is comfortable with all things necessary for understanding GAGA. Moreover, I think the book is well written and therefore definitely a good reference for the analytic world.
A: I would assume that J.P. Serre's GAGA ("Geometrie algebrique et geometrie analytique" modulo some accent marks and possible spelling errors) paper is as still a good a place to start as ever. I've never read it, but it's one of those papers that everyone who has read it says everyone should read. The main results have to do with algebraic sheaves on a variety $X$ and their analytifications on its analytification $X^{an}$. The sheaf cohomology groups on both sides are isomorphic, and I think he might even prove an equivalence of categories with some kind of restriction (coherence?).
