The integral-model intersection conjecture for singular support

Let $X$ be the scheme under consideration, let $\boldsymbol{D}(X)$ denote the relevant derived category, and let $\Lambda$ be an algebraic extension of $\mathbb{Q}_\ell$. For $\mathcal F\in D(X)$, an integral model $\mathcal F_0$ is an integral model of $\mathcal F$ in the sense used in the paper, and $SS(\mathcal F)$ denotes its singular support.

Integral-model intersection conjecture.

$$SS(\mathcal F)=\bigcap SS(\mathcal F_0),$$

where the intersection is taken over all integral models $\mathcal F_0$ for $\mathcal F$.

The statement addresses the difficulty of constructing nontrivial examples in which an integral model has strictly larger singular support than the original sheaf. Its status is not resolved in the supplied text.