9 problems

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 $X$ be a compact set of $\mathbb{R}^d$ that is subanalytic. The quantities $V_i^{\varepsilon}(Y)$ are defined for compact sets $Y$ and parameter $\varepsilon>0$, and the preced…

Kashiwara–Schapira conjecture. Every continuous subanalytic function is almost $\mathcal{C}^{\infty}$-subanalytic.

Let $X=\mathbb{C}^n$, and let $U$ be a relatively compact subanalytic pseudo-convex open subset of $X$. The derived global sections of the sheaf of tempered holomorphic functions,…

Let $M$ be a real analytic manifold, let $U\subset M$ be an open subanalytic subset, and let $\varphi\colon U\xrightarrow[]{}\mathbb{R}$ be continuous and subanalytic on $M$, meani…

Let $X$ be a complex manifold, let $\rho_{\rm sa}$ denote the morphism from the subanalytic site of $X$ to $X$, and let $\rho_{\rm sa!}$, $\rho_{\rm sa}^{-1}$, and $\rho_{\rm sa*}$…

Let $\varphi:X\to Y$ be a proper Thom map, meaning a map equipped with a suitable Whitney stratification satisfying Thom's condition. A triangulation of $\varphi$ is a pair of tria…

Extension conjecture. Theorems 1 and 2 should hold without the assumption that the graph of $f$ is semialgebraic.

Let $X$ be a real-analytic manifold, and let $P^{(1)}$ and $P^{(2)}$ be subanalytic submanifolds with corners. Their associated generalized valuations are denoted by…