In 1972, Iitaka proposed a conjecture which predicts that the subadditivity of Kodaira dimension holds for algebraic fiber spaces in characteristic zero. Although this conjecture has been verified in several important cases, it is still an open problem in general. In this talk, we will discuss the subadditivity of Kodaira dimension in positive characteristic, and will show that one of the natural extensions of Iitaka's conjecture to positive characteristic does not hold.

(This is a talk of Tokyo-Kyoto AG seminar on Zoom, and will be given in Japanese.)