3 problems

Let $\operatorname{Lie}^{\operatorname{perf}}_{\Bbbk}\coloneqq\operatorname{Alg}_{\operatorname{Lie}}(\operatorname{Perf}_{\Bbbk})$ be the $\infty$-category of Lie algebras whose u…

Let $R$ be a complete local ring, and let $F$ be a short complex in the perfect-complex category, meaning a short complex in $\operatorname{perf} R$ supported on the maximal ideal.…

Let $A\to A_0$ be a square-zero extension with kernel $I$, and let $X\to\operatorname{Spec} A$ be a flat Artin stack such that … Write $X_0=X\otimes_A A_0$. Suppose that $P_0$ is a…