bio | website | preschema.com |
---|---|---|
location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 8 months |
seen | Jun 18 at 14:21 | |
stats | profile views | 1,586 |
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. |