7 problems

Let $\mathcal{X}$ be a smooth connected properly stable Artin stack with good moduli space $\pi\colon\mathcal{X}\to X$. Let $A^*_{\operatorname{op}}(X)_\mathbb Q$ be the operationa…

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map, and let $\mathcal {Z}\subseteq\mathcal {X}$ be a generically strong cycle, meaning that every extra component…

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map from a properly stable smooth Artin stack, and let $A^*_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}$ denote its s…

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map from a properly stable smooth Artin stack. Let $e_\mathcal {Z}$ be the generic stabilizer order of a strong cyc…

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map, where $\mathcal {X}$ is a properly stable smooth Artin stack. For a strong cycle $\mathcal {Z}$, let…

Formal GAGA conjecture. If $\mathscr{X}$ has affine diagonal, then the completion functor is an equivalence of categories.

Let $\mathcal{X}$ be a finite type Artin stack over $\operatorname{Spec} k$, and let $xin\robots.txtmathcal{X}(k)$ have linearly reductive stabilizer $G_x$. An algebraic space $X$…