Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthoradeelkh
   • CommentTimeFeb 4th 2015
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexNew entry [[module over a derived stack]] (maybe this is already on some other page?), and some edits to [[perfect complex]].

   New entry module over a derived stack (maybe this is already on some other page?), and some edits to perfect complex.

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeFeb 4th 2015
   • (edited Feb 4th 2015)
   • PermaLink
   Author: Zhen Lin
   Format: MarkdownItexHmmm. So I agree that the abelian category $Qcoh(X)$ is obtained by right Kan extension as you say, by (say) fpqc descent, but surely one needs to know a little bit more to deduce that $\mathbf{D}(Qcoh(X))$ is also obtained by right Kan extension?

   Hmmm. So I agree that the abelian category $Qcoh(X)$ is obtained by right Kan extension as you say, by (say) fpqc descent, but surely one needs to know a little bit more to deduce that $\mathbf{D}(Qcoh(X))$ is also obtained by right Kan extension?

3. • CommentRowNumber3.
   • CommentAuthoradeelkh
   • CommentTimeFeb 4th 2015
   • (edited Feb 4th 2015)
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexI believe $D(QCoh(-))$ also satisfies descent (as a prestack of infinity-categories). I think the original reference is Hirschowitz-Simpson.

   I believe $D(QCoh(-))$ also satisfies descent (as a prestack of infinity-categories). I think the original reference is Hirschowitz-Simpson.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 5th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for starting something on this. I have added some minimum cross-links with _[[module]]_ and _[[quasicoherent sheaf]]_. Presently we have something rough there in the section [quasicoherent sheaf -- in higher geometry](http://ncatlab.org/nlab/show/quasicoherent+sheaf#Higher). All this deserves to be much improved/expanded. Thanks for looking into it. As a trivial comment: we should try to harmonize the titles of these and possible further entries a bit. In fact I think I'll go right now and rename "quasicoherent sheaf" to "quasicoherent sheaf of module".

   Thanks for starting something on this. I have added some minimum cross-links with module and quasicoherent sheaf. Presently we have something rough there in the section quasicoherent sheaf – in higher geometry. All this deserves to be much improved/expanded. Thanks for looking into it.

   As a trivial comment: we should try to harmonize the titles of these and possible further entries a bit. In fact I think I’ll go right now and rename “quasicoherent sheaf” to “quasicoherent sheaf of module”.