All Questions
Tagged with derived-algebraic-geometry simplicial-stuff
8 questions with no upvoted or accepted answers
14
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$E_{\infty}$ $R$-algebras vs commutative DG $R$-algebras vs simplicial commutative $R$-algebras
I've been trying to understand better the relation between the basic blocks of derived algebraic geometry. More precisely, I'm trying to understand the relation between the DG approach, the spectral ...
- 2,227
6
votes
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548
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Resolution of Simplicial Commutative Rings
I have just started learning some derived algebraic geometry. I was told that (if $ \mathrm{char}(\mathbb{K})=0 $) using commutative differential graded algebras in negative degree (for short $ \...
- 79
6
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517
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relative spectrum in derived algebraic geometry
I am trying to understand how much it is possible to extend the notion of spectrum of a qcoh sheaf of algebras to stacks.
More precisely, given a scheme $S$ and a stack $F$ of cohomological cdga's ...
- 121
4
votes
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What does the cotangent complex tell you when it takes animated inputs?
These two links: What is the cotangent complex good for? and Intuition about the cotangent complex? are quite helpful in giving intution for the cotangent complex in terms of deformations but I don't ...
- 301
3
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Homotopy Kan extensions, formally coherent functors and derived Schlessinger criterion
Let $k$ be a finite field. Denote by $discArt_k$ the category of Artinian rings with residue field $k$ and $Art_k$ the category of Artinian simplicial rings. Consider a functor $\mathcal{F}:disArt_k\...
- 4,418
2
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235
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Formally étale maps of animated $k$-algebras
In Lurie's DAG, he defines what it means for a natural transformation $T:\mathcal{F}\to\mathcal{F}'$ of functors $\mathcal{F},\mathcal{F}':\mathcal{SCR}\to\mathcal{S}$ to be formally étale. Namely, it ...
- 301
2
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166
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How to understand $\mathcal{L}BG \simeq G/^{\text{ad}}G$ in term of simplicial sets?
First let $G$ be a topological group and $BG$ its classifying space. Let $\mathcal{L}BG=\text{Map}(S^1, BG)$ be the free loop space of $BG$.
We can see that $\mathcal{L}BG$ has the homotopy type of $...
- 9,019
1
vote
0
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202
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Schlessinger criterion and finiteness of tangent space
Schlessinger's criterion allows us to study whether or not a functor $\mathcal{F}:C_{\Lambda}\rightarrow \text{Set}$ from the category of local Artin $\Lambda$-algebras to sets is representable. One ...
- 4,418