Campana's generalized Lang conjecture

Let (X,i=1r(11mi)Di)(X,\sum_{i=1}^r (1-\frac{1}{m_i})D_i) be a smooth proper C-pair of general type over a number field KK. Let SS be a finite set of finite places of KK, let XSpecOK,S\mathcal{X}\to \operatorname{Spec}\mathcal{O}_{K,S} be a smooth proper model of XX, and let Di\mathcal{D}_i be the closure of DiD_i in X\mathcal{X}. Write

Δ=i=1r(11mi)Di.\Delta =\sum_{i=1}^r\left(1-\frac{1}{m_i}\right)\mathcal{D}_i.

Campana's generalized Lang conjecture. If dimX1\dim X \geq 1, then (X,Δ)(OK,S)(\mathcal{X},\Delta)(\mathcal{O}_{K,S}) is not dense in XX.

This is the orbifold and C-pair analogue of Lang's conjecture on non-density of integral points on varieties of general type. The source gives no resolution.

Sources & referencesView supporting material

Primary source

Finn Bartsch and Ariyan Javanpeykar, “Weakly special varieties, Campana stacks, and Remarks on Orbifold Mordell”, arXiv:2603.28745 (2026).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.