The Zilber--Pink conjecture for products of curves with highly degenerate reduction

We give a proof of the Zilber--Pink conjecture for n-fold self-products of a curve X inside the self-product of its Jacobian, when X has appropriate bad reduction, its Jacobian has no extra endomorphisms, and n is sufficiently small. The strategy of proof follows the work of Katz, Rabinoff and Zureick-Brown on explicit Manin--Mumford bounds.