All Questions

Let $A$ be a local ring of maximal ideal $\mathfrak{m}$. Let $\hat{A}$ be its completion. If $A$ is noetherian , then we know that $A\rightarrow\hat{A}$ is faithfully flat. If $A$ is not noetherian, ...

Notations and background. Let $R$ be a commutative noetherian local ring and let $D(R)$ denote the derived category of the category of R-modules. A strictly perfect complex on $R$ is a bounded complex ...

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, ...