User steven gro - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T01:53:25Z http://mathoverflow.net/feeds/user/24978 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101630/cohomology-groups-interpreted-as-sheafs Cohomology groups interpreted as sheafs Steven Gro 2012-07-08T08:57:20Z 2012-07-08T11:46:19Z <p>Hi Folks,</p> <p>I just came across a few lines where a (sheaf-)cohomology group of a scheme is treated as a sheaf. I've never seen this in Hartshorne. Could you give any reference for this?</p> <p>Thanks</p> <p>Steven</p> http://mathoverflow.net/questions/101630/cohomology-groups-interpreted-as-sheafs/101636#101636 Comment by Steven Gro Steven Gro 2012-07-08T11:16:45Z 2012-07-08T11:16:45Z Thanks for your wonderful answer. Just a small correction: It's Section 8 :-) http://mathoverflow.net/questions/101630/cohomology-groups-interpreted-as-sheafs Comment by Steven Gro Steven Gro 2012-07-08T10:10:43Z 2012-07-08T10:10:43Z Hey Dan, thanks for your answer. To specify my question: The text I am reading is: <a href="http://www.math.utah.edu/~bertram/courses/hilbert/ps/hilbert.ps" rel="nofollow">math.utah.edu/~bertram/courses/hilbert/ps/&hellip;</a> On page 6 Bertram is proving the existence of the hilbert scheme and defines a grassmannian $G(P'(d_0),H^0 (\mathbb{P}^{m}_{A}, \mathcal{O}^{n}_{\mathbb{P}^{m}_{A}} (l + d_0)))$. I think that he is using $H^0 (\mathbb{P}^{m}_{A}, \mathcal{O}^{n}_{\mathbb{P}^{m}_{A}} (l + d_0)))$ as a sheaf, otherwise this notation wouldn't fit his definition of the grassmannian from the beginning of the document. Thanks in advance to all of you!