All Questions

Let $\mathcal M$ be a stack representing some moduli problem. Let $\mathcal X\to \mathcal M$ be the corresponding universal family. What is the difference between the inertia stack $I\to \mathcal M$ ...

Let $S$ be a scheme, and let $f:X\to S$ be a morphism of algebraic spaces. If $f$ is smooth proper curve of genus at least two, then $X$ is a scheme. (Here I mean that $f$ is a smooth proper morphism ...