Lang–Vojta conjecture over function fields for surfaces dominating Gₘ²

We prove the nonsplit case of the Lang–Vojta conjecture over function fields for surfaces of log general type that are ramified covers of Gₘ² G m 2 . This extends the results of Corvaja and Zannier (J Differ Geom 93(3):355–377, 2013), where the conjecture was proved in the split case, and the results of Corvaja and Zannier (J Algebr Geom 17(2):295–333, 2008), Turchet (Trans Amer Math Soc 369(12):8537–8558, 2017) that were obtained in the case of the complement of a degree four and three component divisor in P² P 2 . We follow the strategy developed by Corvaja and Zannier and make explicit all the constants involved.