Timeline for Derived category with total cohomology finite dimensional: is there a better name for it?
Current License: CC BY-SA 2.5
5 events
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| Nov 23, 2009 at 3:57 | history | edited | Greg Stevenson | CC BY-SA 2.5 |
deleted 88 characters in body
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| Nov 22, 2009 at 23:37 | comment | added | Greg Stevenson | By $D_{fd}(A)$ I mean the unbounded derived category of complexes with finite dimensional total cohomology. So it has resolutions, all that removing the superscript here really does is allow one to consider unbounded complexes - one can always truncate above to produce a quasi-isomorphic complex which is bounded above. I don't think this adds anything undesirable (it is not early anymore but my brain isn't really functioning). Although even in the bounded case where you insist all complexes are literally bounded you have an equivalence with $K^{-,b}(A\text{-}proj)$ so you can derive away. | |
| Nov 22, 2009 at 23:24 | comment | added | Ben Webster♦ | Well, mainly I feel deep uncomfortable talking about derived functors in a category where it's not clear I have acyclic resolutions. This is an algebra which does not have finite global dimension, so in $D_{fd}(A)$ objects don't always have projective resolutions in that category, but they do in bounded above. I think the functors I use actually do have acyclic resolutions in the bounded category, but this is not immediately apparent. | |
| Nov 22, 2009 at 21:51 | history | edited | Greg Stevenson | CC BY-SA 2.5 |
fixed silliness
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| Nov 22, 2009 at 21:24 | history | answered | Greg Stevenson | CC BY-SA 2.5 |