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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 28th 2014

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 28th 2014

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.

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeMay 28th 2014
• (edited May 28th 2014)

Affine schemes of algebraic geometry.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 28th 2014

Or close at least. I have added something here.

• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeMay 28th 2014
• (edited May 28th 2014)

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.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJan 17th 2019

• Zachary Maddock, Dolbeault cohomology (pdf)

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.

(?)

• CommentRowNumber7.
• CommentAuthorTim_Porter
• CommentTimeJan 17th 2019

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.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJan 17th 2019
• (edited Jan 17th 2019)

For what it’s worth, I have found and uploaded an old copy of the file (here)