All Questions
10
questions
4
votes
0
answers
175
views
Relation between exotic sheaves in Achar's notes and in Bezrukavnikov-Mirkovic
I am trying to calculate explicitly a certain simple exotic sheaf (a simple object of the heart of the exotic t-structure on the Springer resolution, which is defined in Theorem 1.5.1 of Bezrukavnikov-...
- 2,540
4
votes
0
answers
162
views
External tensor product Calabi-Yau DG categories
Let $\mathcal{C}$ be a smooth proper DG-category such that the shift $[p]$ is a Serre functor for $D^{perf}(\mathcal{C})$ (we say that $D^{perf}(\mathcal{C})$ is $p$-Calabi-Yau). I am looking for a ...
- 7,250
8
votes
0
answers
143
views
Equivariant coherent sheaf category for unipotent group actions
Suppose $U$ is a complex algebraic unipotent group. Let $X$ be a projective variety with a $U$-action. For simplicity, we may assume that there are only finite many $U$ orbits on $X$. The primary ...
- 163
24
votes
0
answers
709
views
What is the status of a result of Kontsevich and Rosenberg?
In their influential paper Noncommutative Smooth Spaces (https://arxiv.org/abs/math/9812158), Kontsevich and Rosenberg define the notion of a noncommutative projective space. In Section 3.3 they ...
- 331
1
vote
0
answers
222
views
Equivariant derived category versus graded derived category
Everything here has the Zariski topology.
Let $T=(\Bbb{C}^*)^d$, and define an action of $T$ on $\Bbb{C}^n$ by $$t\cdot x=(t^{\mathbf{a}_1}x_1,\ldots, t^{\mathbf{a}_n}x_n).$$ Here $\mathbf{a}_1,\...
- 3,039
0
votes
0
answers
330
views
on the Springer sheaf
Let $\pi:\tilde{\mathfrak{g}}\rightarrow \mathfrak{g}$, be the Grothendieck-Springer resolution, where $\mathfrak{g}$ is a semisimple Lie algebra over $\mathbb{C}$.
We know that $\pi$ is small thus $\...
- 3,452
16
votes
1
answer
679
views
Multiplicativity twisted Hochschild Kostant Rosenberg isomorphism
Let $X$ be a smooth projective variety over $\mathbb{C}$. I call (following Swan) Hochschild cohomology of $X$ the graded algebra:
$$ \mathrm{HH}^{\bullet}(X) := \mathrm{Ext}^{\bullet}_{X \times X}(\...
- 7,250
2
votes
1
answer
346
views
Ext groups in the equivariant derived category
I apologize in advance that this question is probably too basic for MO, but I reckoned I would not get an answer on Math.Stackexchange.
I am starting to learn about perverse sheaves, the ...
5
votes
3
answers
1k
views
Exceptional collections with many Exts
Background definitions:
Let $D$ be a triangulated category arising in nature (for instance as the cohomology category of a dg category). An object $E$ in $D$ is called exceptional if $RHom(E,E)$ is ...
- 1,849
7
votes
2
answers
907
views
What is the geometric meaning of reconstruction of quantum group via Ringel Hall algebra
If I remembered correctly. There are some work done by C.M.Ringel,he defined so called Ringel-Hall algebra on abelian category and then show that Ringel-hall algebra is isomorphic to positive part of ...
- 5,435