Timeline for Confusion on summand of Hochschild homology of D-modules
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2019 at 16:54 | comment | added | SashaP | @SamGunningham EBz Yes, you're completely right, I shouldn't have fallen for the commutative intuition. | |
| Feb 17, 2019 at 16:53 | history | edited | SashaP | CC BY-SA 4.0 |
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| Feb 11, 2019 at 17:48 | comment | added | Sam Gunningham | I agree with @EBz, there are many perfect D-modules in the right orthogonal to $\mathcal O$. For another example, take the (clean) extension of a flat connection on $\mathbb A^1- \{0\}$ with non-unipotent monodromy. | |
| Feb 9, 2019 at 11:30 | comment | added | user108998 | I accepted the answer bc I'm now sure compactness of the dg cat is the required condition but I'm still a bit confused by something. It seems \partial can act as an automorphism on a finite type D module. Indeed functions on the punctured line are finite type as a D module and just Fourier transform this? | |
| Feb 8, 2019 at 17:41 | comment | added | SashaP | Another difference from the case of the category of coherent sheaves is that the category in question is not monoidal which might be an issue if we're constructing the left adjoint using duality. | |
| Feb 8, 2019 at 17:39 | history | edited | SashaP | CC BY-SA 4.0 |
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| Feb 8, 2019 at 17:34 | comment | added | SashaP | Sure, I should have swapped them, edited. Yes, it seems that under the assumption that all $H^d(RHom(A,B))$ are finite-dimensional it seems that the semi-orthogonal decomposition on the category of all modules descends to that of the category of perfect modules. | |
| Feb 7, 2019 at 9:46 | comment | added | user108998 | Hi, am I right in saying that you mixed up E and M in the first bit of the answer? Nonetheless it still seems to work. I'm starting to think that the missing assumption is homological compactness of the category, ie the thing that implies finitude of hom spaces. Does this seem correct? This would at least explain all the literature dealing with these decompositions being about proper varieties. | |
| Feb 7, 2019 at 9:46 | vote | accept | CommunityBot | moved from User.Id=108998 by developer User.Id=481663 | |
| Feb 7, 2019 at 9:40 | vote | accept | CommunityBot | moved from User.Id=108998 by developer User.Id=481663 | |
| Feb 7, 2019 at 9:41 | |||||
| Feb 7, 2019 at 5:50 | history | answered | SashaP | CC BY-SA 4.0 |