bio | website | preschema.com |
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location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 4 months |
seen | 11 hours ago | |
stats | profile views | 1,446 |
Jan 16 |
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Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, according to Remark 1.5 in the paper, it seems that the Drinfeld centre of $D(A \otimes A^{op})$ will be the $\infty$-category of modules over the Hochschild chain complex of $A \otimes A^{op}$. |
Jan 14 |
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Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, I think I finally understood what you were really asking. I updated my answer again, let me know if that helps. |
Jan 14 |
revised |
Relationship between Hochschild cohomology and Drinfeld centers
deleted 5 characters in body |
Jan 13 |
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Relationship between Hochschild cohomology and Drinfeld centers
@SamuelM, sorry, I wasn't very clear. I hope the updated answer is more helpful. |
Jan 13 |
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Relationship between Hochschild cohomology and Drinfeld centers
added 1689 characters in body |
Jan 12 |
revised |
Relationship between Hochschild cohomology and Drinfeld centers
deleted 158 characters in body |
Jan 12 |
answered | Relationship between Hochschild cohomology and Drinfeld centers |
Jan 12 |
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Which properties of a variety are detected by its derived category of coherent sheaves?
@მამუკაჯიბლაძე, when taking into account the derived tensor product, one can recover the variety completely (this is a theorem of Thomason and Balmer). |
Jan 12 |
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Which properties of a variety are detected by its derived category of coherent sheaves?
As far as I know, it is not possible to recover the derived category of quasi-coherent complexes from the bounded derived category of coherent sheaves, at the triangulated level. At the level of infinity- or dg-categories, one can recover it as the ind-objects (in the regular case). |
Jan 12 |
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Which properties of a variety are detected by its derived category of coherent sheaves?
The derived category detects homological invariants like (higher) algebraic K-theory, Hochschild homology, cyclic homology, etc. As for cohomological invariants, it is a theorem of Orlov that these are detected up to Tate twists in general, and in some special cases detected completely. |
Dec 18 |
awarded | Popular Question |
Dec 11 |
awarded | Yearling |
Nov 27 |
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Site dependance of the Cech weak equivalences on simplicial sheaves
Just to be clear: you are asking if the weak equivalences in the model structure(s) described at ncatlab.org/nlab/show/… can be described independently of the site of definition, right? |
Nov 17 |
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Use of derivators to the theory of motives?
more appropriate tags |
Nov 17 |
suggested | approved edit on Use of derivators to the theory of motives? |
Nov 17 |
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Use of derivators to the theory of motives?
However, a beautiful idea of Ayoub is to modify the definition of derivator, replacing the 2-category of diagrams by the 2-category of diagrams of schemes over some base, and imposing various axioms. The resulting notion, which he calls an algebraic derivator, essentially captures the whole formalism of six functors. I am not sure, but I believe that Grothendieck probably did not have anything like this in mind when he wrote Pursuing Stacks or Les Derivateurs (and I will be very happy if an expert could confirm). |
Nov 17 |
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Use of derivators to the theory of motives?
In the motivic world, model categories and infinity-categories are used as refinements of triangulated categories. These are "stronger" refinements than derivators (in some precise sense), so I doubt that the theory of derivators can offer any improvements to the theory of motives. |
Nov 11 |
awarded | Nice Answer |
Nov 11 |
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A bestiary of topologies on Sch
Hi Pieter, I guess I should have waited for you to finish it and post it here yourself then! Still, I find it an invaluable resource already, so thanks a lot :) |
Nov 11 |
awarded | Necromancer |