39 problems

Let $X$ be a closed subscheme of a smooth scheme over a perfect field $k$, and let $\mathcal{F}$ be a constructible complex of $\Lambda$-modules of finite Tor-amplitude on $X$. Let…

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…

Let $\mathbb{T}_0$ be the punctured torus, and let $D^\pi\mathcal{F}(\mathbb{T}_0)$ denote the split-closed derived Fukaya category of $\mathbb{T}_0$. Let the constructible plumbin…

Constructibility conjecture. The complex $\mathcal{S}ol^{<0}(\mathcal{M})$ has $\mathbb{C}$-constructible cohomology sheaves.

Let $G$ be a reductive algebraic group, and let ${\cal F}$ be a constructible sheaf on $G$ that is equivariant under the adjoint action. The preceding result asserts nonnegativity…

Let ${\mathfrak{f}}=\overline{\mathbb{F}}_p((t))$ and ${\mathfrak{o}}=\overline{\mathbb{F}}_p[[t]]$. Let $G$, $X$, and $Y$ be the group and the two $G$-spaces described above, and…

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 $T^n$ be the $n$-torus, let $R_n$ be the ring appearing in the paper, and let $M$ be an $R_n$-module. Suppose that a constructible sheaf…

Let $X$ be a toric variety, and let the associated Lagrangians in cotangent bundles of tori and Euclidean spaces define a microsupport condition on sheaves. FLTZ conjecture. The ca…

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…

The category of $\mathcal D$-modules is abelian, while the derived category of constructible sheaves is not. An abelian subcategory of the derived category that receives the soluti…

Let $f\colon X\to Y$ be a proper morphism of smooth schemes over a perfect field $K$, with $X$ of dimension $n$ and $Y$ of dimension $m$, and let $\mathcal F$ be a constructible co…

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 $k$ be an algebraically closed field, let $X$ be a projective variety with an action of a linear algebraic group $G$, and suppose that $X$ has finitely many $G$-orbits. Let…

Let $X$ and $S$ be complex manifolds, let $p_X:X\times S\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow} X$ be the projection, and let…

Let $X$ and $Y$ be locally noetherian fs log adic spaces, and let $f:Y\rightarrow X$ be a proper and log smooth morphism. Let $\Lambda$ be a noetherian torsion ring, and let…

Let $X=\mathrm{Spa}\,A$ be an affinoid rigid space, let $\mathcal{X}=\mathrm{Spec}\,A$, and let … be the natural morphism of sites. Write $\Lambda$ for the coefficient ring, and le…

Let $L$ be an algebraically closed field and let $Z$ be an $L$-variety. Consider an object $\operatorname{\mathscr{F}}\in\mathcal{D}^b(Z_{\text{ét}},\Lambda)$, where $\Lambda$ is t…

In the setting of non-Archimedean geometry, let semi-constructible sheaves be the class of sheaves introduced in the paper, and let reflexive sheaves be those identified with their…

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…