Grothendieck–Katz p-curvature conjecture

In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case. It is a conjecture of Alexander Grothendieck from the late 1960s, and apparently not published by him in any form.

The general case remains unsolved, despite recent progress; it has been linked to geometric investigations involving algebraic foliations.