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Oct 27, 2023 at 2:00 vote accept Richard
Oct 26, 2023 at 20:33 answer added Oli Gregory timeline score: 2
Oct 23, 2023 at 4:49 comment added Oli Gregory The answer is no. In fact the relationship between different liftings $X$ of $Y$ and different liftings of the Hodge filtration is often very interesting. The classic example, I think, is if your $Y$ is an abelian variety of dimension $g$. In that case the liftings of $Y$ are in bijection with liftings of the Hodge filtration which are isotropic with respect to the cup product on $H^{1}_{cris}$.
Oct 23, 2023 at 3:41 history asked Richard CC BY-SA 4.0