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have added a tad more content to Stein manifold and cross-linked a bit more
Added the statement of Cartan’s theorem B and added to the Idea-section a remark that therefore Stein manifolds play the role in complex geometry of Cartesian spaces in smooth manifold theory, for purposes of abelian (Cech)-sheaf cohomology.
Affine schemes of algebraic geometry.
Or close at least. I have added something here.
I am not saying that (about the analytification), but precisely what you say above: affine are cohomologically trivial in the sense as proved in chapter 3 of Hartshorne’s book and this is a usually given statement when algebraic geometers look at analytic spaces. Many other deep properties are also analogous.
somebody just alerted me:
this page here has been and still is referring to
for proof of some of its statements (existence of “good” Stein covers). However, the link to that pdf
http://www.math.columbia.edu/~maddockz/notes/dolbeault.pdf
no longer works, and Google seems to see no other trace of it either.
(?)
Zachary Maddock is on Linkedin so you might be able to contact him and put a copy of the document on the Lab if it seems worth it.
For what it’s worth, I have found and uploaded an old copy of the file (here)
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