All Questions

Let $X\rightarrow S$ be a proper flat morphism of schemes. When is the cotangent complex $L_{X/S}$ perfect ? It is well known, that for local complete intersections the cotangent complex is perfect, ...

In the stacks project, there is a 'naive version' of cotangent complex $NL_{S/R}$ for a ring morphism $R\rightarrow S$, given by the chan complex $(I/I^{2}\rightarrow \Omega_{R[S]/R}\otimes_{R[S]}S)$ ...

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 ...

I am interested in the concept of dimension of derived and $n$-Artin stacks. Take for example the definition 4.10 of From HAG to DAG: derived moduli stacks. in which they define the dimension of a ...

$\DeclareMathOperator\Sym{Sym}\DeclareMathOperator\Spec{Spec}$If $V$ is a dg vector space (in positive degrees), we can view it as a derived scheme $V = \Sym V^*$. It has (co)tangent complex $V$ (and $...