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Results tagged with ag.algebraic-geometry
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user 2503
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
gluing of DG-categories
As mentioned in the comments, we need to fix isomorphisms $\newcommand{\D}{\mathscr{D}}\D_1 \xrightarrow{\sim} \D_1^{op}$ and $\D_2 \xrightarrow{\sim} \D_2^{op}$ for the question to make sense.
They k …
- 5,901
2
votes
0
answers
4k
views
Automorphisms of projective space [closed]
According to Wikipedia, Aut(P(V)) = PGL(V). Apparently this is proved by using sheaves generated by global sections but I'm not familiar with this notion. I would appreciate it if anyone could provi …
- 5,901
9
votes
Basic questions about stacks 2
Regarding 3), Andrew Kresch just told me that they gave up on the project.
- 5,901
9
votes
References for the "nerve of an algebraic variety"
One way to understand your question is in the framework of $\mathbf{A}^1$-homotopy theory. This is because your nerve functor is better understood when defined on a cocomplete category like the categ …
- 5,901
6
votes
Accepted
Do algebraic stacks satisfy fpqc descent?
It may be helpful to have a look at these notes by Anatoly Preygel (see also MO/15910/2503). In particular, Proposition 3.3.6 says that an algebraic stack is an fpqc sheaf if the diagonal is quasi-af …
- 5,901
3
votes
Accepted
When is a sheaf coherent if its image under a Fourier-Mukai transform is coherent?
Your proof works in the derived case as well.
That is, assume smoothness so that $D^bCoh$ is identified with the full subcategory of compact objects (in general the argument will apply to the subcate …
- 5,901
3
votes
Accepted
For what varieties do we have results on the category of singularities?
A student of Orlov is working on one case. He will give a talk in two weeks in Padova, here is the abstract:
Oleksandr Kravets (Moscow Higher School of Economics, Russia), Exceptional collections i …
- 5,901
41
votes
A bestiary of topologies on Sch
I have just discovered a chart comparing topologies on Sch/S, made by Pieter Belmans. It includes all the topologies discussed above, and some more I haven't even heard of. It's even interactive and …
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83
votes
Accepted
Derived algebraic geometry: how to reach research level math?
I propose the following plan, assuming a basic background in scheme theory and algebraic topology. I assume that you are interested in derived algebraic geometry from the point of view of application …
22
votes
Accepted
Why is "naive" definition of non-commutative spectrum bad?
I have also wondered about this question and recently came across some papers that seem to answer it.
First of all, the paper
Manuel L. Reyes, Obstructing extensions of the functor Spec to noncommu …
- 5,901
16
votes
DG categories in algebraic geometry - guide to the literature?
There are plenty of interesting dg-categories one can associate to a scheme. From the point of view of six functor yoga, these should be viewed as "categories of coefficients" for cohomology theories …
- 5,901
2
votes
Accepted
Integral transform on noncommutative spaces
Let $DGCat_k$ denote the $\infty$-category obtained by localizing the category of dg-categories at Morita equivalences. This is presented by the Morita model structure on the category of dg-categorie …
- 5,901
8
votes
Accepted
Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left?
The exact sequence of triangulated categories
$$ Perf(X)\to D^b_{coh}(X)\to D_{sg}(X) $$
may be lifted to an exact sequence of stable $\infty$-categories or dg-categories in the sense of BGT: choose …
- 5,901
8
votes
Accepted
Relations between Motivic Galois groups and Motivic t-structure?
The argument sketched in Example 3.20 of [J. P. Pridham, Tannaka duality for enhanced triangulated categories, arXiv:1309.0637] demonstrates the comparison assuming the existence of the motivic t-stru …
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17
votes
Why is the motivic category defined over the site of smooth schemes only?
It makes sense to consider larger versions of the (unstable and stable) motivic homotopy categories built out of the site $Sch_S$ of all schemes over $S$ (say of finite type to avoid dealing with size …
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