Develops canonical bundle formulas for separable and inseparable fibrations of curves with arithmetic genus one in char p>0 and proves that certain klt pairs with nef anti-canonical bundle are fiber spaces over their Albanese variety when the morphism has relative dimension one.
Hacon, Zsolt Patakfalvi, and Lei Zhang, Birational characterization of Abelian vari- eties and ordinary Abelian varieties in characteristic p > 0, Duke Math
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On canonical bundle formula for fibrations of curves with arithmetic genus one
Develops canonical bundle formulas for separable and inseparable fibrations of curves with arithmetic genus one in char p>0 and proves that certain klt pairs with nef anti-canonical bundle are fiber spaces over their Albanese variety when the morphism has relative dimension one.