Ekedahl–Shepherd-Barron–Taylor–Bost algebraicity conjecture for foliations

Let $R\subset\mathbb{C}$ be a finitely-generated $\mathbb{Z}$-algebra, and let $M$ be a smooth $R$-scheme. A foliation $\mathscr{F}\subset T_{M/R}$ is a sub-bundle of Lie algebras. Vanishing $p$-curvature means that $\mathscr{F}\bmod p$ is closed under $p$-th powers mod $p$. Ekedahl–Shepherd-Barron–Taylor–Bost conjecture. The complex-analytic leaves of $\mathscr{F}$ are analytifications of algebraic subvarieties of $M_{\mathbb{C}}$ if and only if $\mathscr{F}\bmod p$ is closed under $p$-th powers mod $p$ for almost all primes $p$, equivalently, it has vanishing $p$-curvature. This is the foliated analogue of the Grothendieck–Katz conjecture and is used as the conceptual framework for the paper's non-abelian isomonodromy results; the source does not state a general resolution.