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Questions tagged [cotangent-complex]

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Why does the cotangent complex really have a distinguished triangle?

Associated to any ring maps $A\to B\to C$ there is the distinguished triangle $$\mathbf{L}_{B/A}\otimes^L_BC\ \longrightarrow \ \mathbf{L}_{C/A} \ \longrightarrow \ \mathbf{L}_{C/B} \ \stackrel{+1}{\...
7
votes
0answers
289 views

Computer Algebra solution for simplicial resolutions for André-Quillen cohomology

Hello, I would like to experiment with André-Quillen (co)homology. Especially for singular rings. A key problem is that the construction of a simplicial resolution of a ring seems to require a rather ...
6
votes
0answers
331 views

Explicit computation of the cotangent complex in a non-lci case

Is there an example of a non-lci morphism $X\rightarrow Y$ for which the entire cotangent complex (or just Andre-Quillen cohomology) can be explicitly computed? I believe it is a theorem of Avramov ...
5
votes
0answers
230 views

Flat Connections on the Cotangent Complex

I'm trying to find a reference which defines and discusses some properties of connections and flat connections on the cotangent complex in a homotopical setting. That is to say, a connection or flat ...
3
votes
0answers
122 views

Does the cotangent complex commute with coequalisers?

I would like to know if the cotangent complex (say of rings) commutes with coequalisers. More precisely, let $B_1\rightrightarrows B_2\rightarrow C$ be a coequaliser of $A$-algebras. Is then the ...
2
votes
0answers
141 views

Comparing definitions of cotangent complex

Consider the following two ways of defining the cotangent complex of a ring map $R \rightarrow A$ (Let $P^{\bullet} \rightarrow A$ be a polynomial resolution): As the complex $\Omega^1_{P^{\bullet}/R}...
1
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71 views

Question about $\Delta(n)_{U}$ notaion in illusie's cotangent compelexe et deformations

In illusie's book cotangent complexe et deformations, 38page, the notation $\Delta(n)_{U}$ appears, and I cannot find the direct explanation or hint about meaning of this notation in this book. I ...