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I'm just beginning my second year as a graduate student. I know a bit of complex geometry and a bit of algebraic geometry. The lack of rigor in my understanding of the connection of the two is growing a bit frustrating, so I'd like to learn about analytification and so on. I'm sure Serre is good, but I suspect I'd appreciate a more recent exposition (preferably in English).

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  • $\begingroup$ There is a translation of GAGA. Math never becomes out of date, and it wasn't written that long ago in the grand scheme of things, so it may be worth a shot. $\endgroup$ Sep 21 '19 at 15:11
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    $\begingroup$ For a readable introduction by a master, check out Griffiths and Adams, Algebraic and Analytic Geometry (Princeton yellow). $\endgroup$ Sep 22 '19 at 0:45
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There is the book Algebraic and Analytic Geometry by Neeman which focuses on GAGA and is very detailed. It starts with basics in manifold and scheme theory, continues with analytification and ends with GAGA theorems of varying/increasing generality as far as I remember. I guess this might be the reference that you were searching for.

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  • $\begingroup$ Read the introduction.. if you think it is not well written, leave it.. I bet you will not leave it :D I read introduction just after seeing this answer.. this book is a masterpiece for advanced undergraduate students... $\endgroup$ Sep 21 '19 at 19:36

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