We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for -factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.
"Minimal models and abundance for positive characteristic log surfaces." Nagoya Math. J. 216 1 - 70, December 2014. https://doi.org/10.1215/00277630-2801646