12 problems

Let $X$ be a smooth $p$-adic analytic Artin stack, and let $L(X)$ denote its associated light condensed anima. Clausen's conjecture. Étale-locally, $L(X)$ is a light profinite anim…

Light profiniteness conjecture. Étale locally, the associated light condensed anima is a light profinite anima.

Let $Y$ be an irreducible $\mathbb{Q}$-Gorenstein variety, and let … be a crepant resolution such that $\mathcal{X}$ has affine diagonal. Optimality conjecture for crepant resoluti…

A weak K-moduli space is an Artin stack when continuous isotropy is allowed. Consider such a stack parametrizing polarized irreducible holomorphic symplectic varieties, polarized a…

Let $K$ be a finite extension of $\mathbb Q_p$, let $\mathcal O_K$ be its ring of integers, and let $\mathpzc X$ be a smooth formally proper Artin stack over $\mathcal O_K$. Let…

Special-stabilizer lifting conjecture. If all stabilizers of $\mathcal{X}$ are special groups, then $\operatorname{sep}_\pi^{-1}(0) \subset \mathscr{L}(X)$ is measurable and

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…

Let $\mathcal {X}$ be a properly stable smooth Artin stack with good moduli space ${\mathbf X}$. The strong relative Chow groups $A^k_{st}(\mathcal {X}/{\mathbf X})$ are generated…

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…

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 $X$…

Alper's étale-local quotient conjecture. There exists an étale neighborhood $S'\to S$ with $s'\mapsto s$ and an étale, representable morphism