16 problems

Let $\Xfr$ be a smooth semiprojective toric variety. The category $\Sh_{\Lambda_\mathrm{Cox}}(M_\RR / M)$ is closed under $\otimes_k$. Cox category tensor-product conjecture. There…

Lagrangianity conjecture. $SS(\mathcal{F})$ is an analytic Lagrangian subspace of $T^*X$, meaning that it is an analytic closed subset and is Lagrangian on its regular locus. In pa…

Microlocal endomorphism conjecture.

Complex-constructible wrapping conjecture. For every object $\mathcal E$ of $\Sh_{\mathbb C\text{-}c}(M)$, there exists an inductive system $\{\mathcal E_i\}$ in…

Let $U\subset X$ be complex manifolds satisfying the conditions in Theorem. Let $\mathcal F\in D^b_c(X,A)$ be a constructible complex such that $\mathcal F|_U\neq 0$. Non-vanishing…

Let $f:X\to Y$ be a cylindrically stratified morphism of stratified topological spaces. A morphism is compactifiable if it factors as a stratified open embedding followed by a prop…

Let $K$ be a quasicategory in which all endomorphisms are equivalences. Write $||K||$ for its stratified realization, and let $C_*K$ denote the chain complex associated to $K$. Exi…

Let $X$ be a complex algebraic variety. Let $\C_X$ be $Perv(X,\mathbb{C})$ or $\mathbf{D}^b_c(X,\mathbb{C})$, and let $S=\{\mathcal{F}\}\subset\operatorname{Iso}(\C_X)$ consist of…

Fix a finite field $\mathbb{F}$ and let $\mathcal{L}_{\mathbb{F}}(n,D,\kappa)$ consist of pairs $(X,[\mathcal{F}])$, where $X$ is an Alexandrov space of Hausdorff dimension at most…

Fix a finite field $\mathbb{F}$. Let $X$ be a compact Alexandrov space, and let $D^b_c(\operatorname{Sh}_{\mathbb{F}}(X))$ denote the bounded derived category of constructible shea…

Characteristic-cycle push-forward conjecture. We have

Let $X$ be a complex manifold, let $\mathcal{D}_X$ be its sheaf of differential operators, and let $\mathcal{M}\in D^b_h(\mathcal{D}_X)$ be a bounded complex with holonomic cohomol…

For a sequence of constructible sheaves in the real sheaf-theoretic polynomial hierarchy $\boldsymbol{\mathcal{PH}}_\mathbb{R}$, let…

For each positive integer $p$, let $\boldsymbol{\Lambda}^{(p)}\boldsymbol{\mathcal{P}}_\mathbb{R}$ denote the $p$-th sheaf-theoretic quantifier level built from…

Nadler–Tanaka's stratified constructible-sheaf conjecture. There is a canonical equivalence of stable $\infty$-categories

Nadler–Tanaka's constructible-sheaf conjecture. There is a canonical equivalence of stable $\infty$-categories