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1. • CommentRowNumber1.
   • CommentAuthorMatanP
   • CommentTimeJun 20th 2012
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   Author: MatanP
   Format: MarkdownItexDo anyone here knows of works that study higher (preferably infinity) versions of dualizing complexes? Thanks in advance..

   Do anyone here knows of works that study higher (preferably infinity) versions of dualizing complexes?

   Thanks in advance..

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJun 22nd 2012
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   Author: zskoda
   Format: MarkdownItexWhat is the application you have in mind ? I am sure nobody done for $(\infty,m)$ for $m\gt 1$, while for most applications $(\infty,1)$ does not buy you much over the traditional derived picture and it is probably kind of worked out (not buying much by theorem of Orlov/Lunts on uniqueness of enhancements in most geometric contexts).

   What is the application you have in mind ? I am sure nobody done for $(\infty,m)$ for $m\gt 1$, while for most applications $(\infty,1)$ does not buy you much over the traditional derived picture and it is probably kind of worked out (not buying much by theorem of Orlov/Lunts on uniqueness of enhancements in most geometric contexts).

3. • CommentRowNumber3.
   • CommentAuthorMatanP
   • CommentTimeJun 22nd 2012
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   Author: MatanP
   Format: MarkdownItexWell, I don't have specific application in mind but I have the general feeling that Verdier's theory of derived categories can all be "lifted" from the homotopy category to stable infinity-categories. Of course much have been done in this direction with (stable) model structures on complexes etc., but I was wondering specifically about dualizing complexes because it wasn't clear to me how such a thing will go. Nevertheless, can you name the paper/thm of Orlov/Lunts you had in mind?

   Well, I don’t have specific application in mind but I have the general feeling that Verdier’s theory of derived categories can all be “lifted” from the homotopy category to stable infinity-categories. Of course much have been done in this direction with (stable) model structures on complexes etc., but I was wondering specifically about dualizing complexes because it wasn’t clear to me how such a thing will go. Nevertheless, can you name the paper/thm of Orlov/Lunts you had in mind?

4. • CommentRowNumber4.
   • CommentAuthorMatanP
   • CommentTimeJun 22nd 2012
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   Author: MatanP
   Format: MarkdownItexLet me try and sharpen the question: suppose for simplicity that we take d.c.'s over a fixed ring. then we get a subinfinity-category of the category C(A Mod) of complexes of A-modules. We can then try and "lift" theorems on dualizing complexes that were traditionally phrased in terms of the homotopy category and get their infinity versions (e.g. by using the different model structures). I would like to know of works that took such a path.

   Let me try and sharpen the question: suppose for simplicity that we take d.c.’s over a fixed ring. then we get a subinfinity-category of the category C(A Mod) of complexes of A-modules. We can then try and “lift” theorems on dualizing complexes that were traditionally phrased in terms of the homotopy category and get their infinity versions (e.g. by using the different model structures). I would like to know of works that took such a path.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJun 23rd 2012
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   Author: zskoda
   Format: MarkdownItexUsually similar work is in terms of A-infinity categories, rather than in a bit further simplicial language.

   Usually similar work is in terms of A-infinity categories, rather than in a bit further simplicial language.

6. • CommentRowNumber6.
   • CommentAuthorMatanP
   • CommentTimeJun 24th 2012
   • (edited Jun 24th 2012)
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   Author: MatanP
   Format: MarkdownItexone interesting thing is that although the full sub-infinity-category of all dualizing complexes (over, say, a noetherian ring) is not stable (while the category of complexes is), it is almost stable in that d.c.'s are unique up to a shift and a tensor by an invertible.

   one interesting thing is that although the full sub-infinity-category of all dualizing complexes (over, say, a noetherian ring) is not stable (while the category of complexes is), it is almost stable in that d.c.’s are unique up to a shift and a tensor by an invertible.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2013
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   Author: Urs
   Format: MarkdownItexJust for the record: In [[E-infinity geometry]] higher dualizing complexes are discussed in section 4.2 of Lurie's _[[Representability theorems]]_

   Just for the record:

   In E-infinity geometry higher dualizing complexes are discussed in section 4.2 of Lurie’s Representability theorems

8. • CommentRowNumber8.
   • CommentAuthorMatanP
   • CommentTimeDec 5th 2013
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   Author: MatanP
   Format: MarkdownItexThanks!

   Thanks!