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bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 6 months
seen Jun 18 at 14:21

Jan
12
answered Relationship between Hochschild cohomology and Drinfeld centers
Jan
12
comment 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
comment 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
comment 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
comment 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
revised 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
comment 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
comment 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
comment 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
Nov
11
answered A bestiary of topologies on Sch
Nov
10
comment Etale topos as a classifyng topos ?
The question is answered in arxiv.org/pdf/0902.1130v2.pdf (though surely known much earlier).
Nov
8
comment Mysterious quotes (at least for me)
Right, I should have said derived Morita invariance. And Orlov's remark was about the derived category of a commutative scheme.
Nov
7
awarded  Enlightened
Nov
7
awarded  Nice Answer
Nov
6
comment why are motives more serious than “naive” motives?
@VivekShende, Chow motives are supposed to be the semisimple objects in the abelian category of mixed motives (whose derived category is supposed to coincide with Voevodsky's DM). There is a functor from Chow motives to DM which is known to be fully faithful.