This is a continuation of , where it was shown that K-equivalent complex projective manifolds have the same Betti numbers by using the theory of p-adic integrals and Deligne's solution to the Weil conjecture. The aim of this note is to show that with a little more book-keeping work, namely by applying Faltings' p-adic Hodge Theory, our p-adic method also leads to the equivalence of Hodge numbers — a result which was previously known via motivic integration.
"Cohomology Theory in Birational Geometry." J. Differential Geom. 60 (2) 345 - 354, February, 2002. https://doi.org/10.4310/jdg/1090351105