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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2014

    have added a tad more content to Stein manifold and cross-linked a bit more

    • 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

    somebody just alerted me:

    this page here has been and still is referring to

    • 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.

    (?)

    diff, v12, current

    • 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)

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