An example of liftings with different Hodge numbers
Does a smooth proper variety in positive characteristic know the Hodge numbers of its liftings? The answer is "of course not". However, it's not that easy to come up with a counter-example. In this talk, I will first introduce the background of this problem. Then I shall discuss some obvious constraints of constructing a counter-example. Lastly I will present such a counter-example and state a few questions of similar flavor for which I do not know an answer.