Kobayashi-Ochiai's theorem states that the set of dominant rational maps from a complex variety to a complex variety of general type is finite. Kazuya Kato conjectured a similar result in the category of log schemes. Our main theorem of this paper is a solution to his conjecture.
"Dominant rational maps in the category of log schemes." Tohoku Math. J. (2) 59 (4) 481 - 525, 2007. https://doi.org/10.2748/tmj/1199649872