An example of liftings with different Hodge numbers 
-- Shizhang Li, February 15, 2019

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Does a smooth proper variety in positive characteristic know the
Hodge number 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 further question.