%0 Journal Article %T A note on the characteristic $p$ nonabelian Hodge theory in the geometric case %A Mao Sheng %A Xin He %A Kang Zuo %J Mathematics %D 2012 %I arXiv %X We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result. %U http://arxiv.org/abs/1202.3942v3