Abstract
In characteristic 0, the Campana-Peternell conjecture claims that the only smooth Fano variety with nef tangent bundle should be homogeneous. In this paper, we study the positive characteristic version of the Campana-Peternell conjecture. In particular, we give an affirmative answer for Fano 4-folds with nef tangent bundle and Picard number greater than one.
Acknowledgments
The authors would like to thank an anonymous referee for his/her useful comments. In particular, he/she noted that the computational part of Proposition 3.3 follows from the same argument as [Citation21, Lemma 5.1].