bio | website | preschema.com |
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location | Essen, Germany | |
age | 23 | |
visits | member for | 5 years, 1 month |
seen | 1 hour ago | |
stats | profile views | 1,246 |
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 |
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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. |
Nov 6 |
revised |
Mysterious quotes (at least for me)
added 10 characters in body |
Nov 6 |
revised |
Mysterious quotes (at least for me)
added 30 characters in body |
Nov 6 |
answered | Mysterious quotes (at least for me) |
Nov 3 |
comment |
Does “simplicial” commute with “Bousfield localization”?
Of course, this has nothing to do with $\Delta$ and works more generally for presheaf (∞-)categories. |
Nov 2 |
revised |
Why higher category theory?
add higher-category-theory tag |
Nov 2 |
suggested | approved edit on Why higher category theory? |
Nov 2 |
comment |
Why higher category theory?
See the closely related question mathoverflow.net/questions/169187/…. |