%0 Journal Article %T The X-method for klt surfaces in positive characteristic %A Hiromu Tanaka %J Mathematics %D 2012 %I arXiv %X In this paper, we establish a weak version of the Kodaira vanishing theorem for surfaces in positive characteristic. As an application, we obtain some fundamental theorems in the minimal model theory for klt surfaces. %U http://arxiv.org/abs/1202.2497v2