All Questions
7 questions
5
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What classifies deformations of group schemes (or Hopf algebras)?
The cotangent complex of a scheme classifies its deformations.
That is, if $X$ is a scheme over a field $k$ (with conditions?) and $\mathbf{T}^*_X\in D^b(\text{QCoh}(X))$ its cotangent complex, the ...
- 5,701
3
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0
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164
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Linear deformations of a morphism between stacks
Given smooth algebraic stacks $\mathcal{X}$, $\mathcal{Y}$ what are the linear deformations $\operatorname{Def}^1(f: \mathcal{X} \to \mathcal{Y})$ of a morphism $f:\mathcal{X} \to \mathcal{Y}$?
In ...
- 163
3
votes
0
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214
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formal smoothness and cotangent complex
If $k$ is a field and $A$ is a formally smooth $k$-algebra, then we know that $\Omega^{1}_{A/k}$ is projective. What about its cotangent complex $L_{A/k}$? When is it quasi-isomorphic to $\Omega^{1}_{...
- 3,472
15
votes
1
answer
770
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Cotangent Complex in Analytic Category
I am looking for a reference which develops the theory of the cotangent complex for complex analytic spaces. I need this to justify some computations I did assuming some formal properties which hold ...
- 1,761
8
votes
1
answer
2k
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Elementary (English) reference for the cotangent complex?
I'm trying to understand cotangent complexes and their role in deformation theory, and later the statement that they're somehow natural in a derived scheme/stack.
I understand that the standard ...
- 83
17
votes
1
answer
846
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Are deformations of a scheme some kind of a "derived gerbe" under the cotangent complex?
(This is probably a very naive question. My understanding of the cotangent complex is quite vague.)
Let me first recall the picture for deformations of a smooth morphism:
If $f:X_0\to S_0$ is a ...
- 16.1k
64
votes
5
answers
9k
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Intuition about the cotangent complex?
Does anyone have an answer to the question "What does the cotangent complex measure?"
Algebraic intuitions (like "homology measures how far a sequence is from being exact") are as welcome as ...
- 12.3k