We study the deformation theory of elliptic fiber bundles over curves in positive characteristics. As applications, we give examples of nonliftable elliptic surfaces in characteristics 2 and 3, which answer a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.
"Deformations of elliptic fiber bundles in positive characteristic." Nagoya Math. J. 211 79 - 108, September 2013. https://doi.org/10.1215/00277630-2141608