All Questions

$\DeclareMathOperator\C{\mathbf{C}}$Motivation: this post discusses a simple criterion for a 1-parameter family of $n$-dimensional complex algebras to be a "trivial deformation", i.e., be ...

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}_{...

Let $k$ be an algebraically closed field, $A\rightarrow B$ be a continuous map of weakly admissible topological $k$-local algebras. We assume that it is formally smooth and topologically of finite ...

Let $k$ be some field, algebraically closed and of characteristic $0$, if you like. Let $U= \mathbb{A}^2_k \setminus \{ (0,0) \}$ be the punctured affine plane over $k$. Write $U$ as the union of $...