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bio website preschema.com
location Essen, Germany
age 23
visits member for 5 years, 3 months
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Jan
1
answered gluing of DG-categories
Jan
1
comment gluing of DG-categories
You need to be able to identify the dg-categories with their respective opposite categories. For example it would make sense for dg-categories of sheaves on a scheme, where you have duals ($E \mapsto \mathbf{R}\mathrm{Hom}(E, O_X)$).
Jan
1
comment gluing of DG-categories
How exactly are you defining $\varphi^\mathrm{op}$?
Dec
30
comment V.I. Arnold's high school problem
This is a very easy olympiad problem. Take a look at "The USSR olympiad problem book", you'll be surprised at what else Russian twelve-year olds can do.
Dec
30
answered Maps to projective space determined by a line bundle
Dec
26
comment K-theory of complete intersection
Perhaps the title should be changed to "Grothendieck group of..." instead of "K-theory of...".
Dec
23
comment A statement for a triangulated category generated by a subset
As soon as the inclusion admits a right adjoint, there is a canonical equivalence of categories $\left<A\right>^\perp \stackrel{\sim}{\to} D/\left<A\right>$. Also $\left<A\right>$ is automatically thick under this assumption. See section 1.2 of Beilinson-Vologodsky for a reference.
Dec
21
comment Reconstructing the Chow ring from the derived category
@SébastienPalcoux, this is noncommutative geometry in the sense of Kontsevich, when one replaces a variety by the triangulated category of perfect complexes on it.
Dec
19
comment Is Euclid dead?
@MonroeEskew, sadly, I doubt you will see a proof of these things in a high school geometry course (in the US, at least; I think the Russian curriculum is another story).
Dec
19
comment Reconstructing the Chow ring from the derived category
@Sasha, thanks, but I consider $\mathbf{D}(X)$ without the tensor structure.
Dec
19
comment Reconstructing the Chow ring from the derived category
@ya-tayr, good point, you only get the ring structure on $\mathrm{CH}_*(X)$ when you consider the monoidal structure on $\mathbf{D}(X)$.
Dec
19
revised Reconstructing the Chow ring from the derived category
added 22 characters in body
Dec
19
revised Reconstructing the Chow ring from the derived category
added 130 characters in body
Dec
19
asked Reconstructing the Chow ring from the derived category
Dec
14
awarded  Necromancer
Dec
14
awarded  Yearling
Dec
14
revised Stable infinity categories vs dg-categories
added 786 characters in body
Dec
12
comment Derived Category.
It may be helpful to think first about the corresponding questions in the "baby" case of homological algebra, i.e. modules over a commutative ring.
Nov
15
answered Stable infinity categories vs dg-categories
Oct
21
comment About the category of chain complexes and Grothendieck categories.
See also the nlab page: ncatlab.org/nlab/show/…