Geodesic
The construction problem for Hodge numbers modulo an integer in positive characteristic
Forum of Mathematics, Sigma, Tome 8 (2020)

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Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$, we show that the Hodge numbers of a smooth projective k-variety can take on any combination of values modulo m, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers. 
@article{10_1017_fms_2020_48,
     author = {Remy van Dobben de Bruyn and Matthias Paulsen},
     title = {The construction problem for {Hodge} numbers modulo an integer in positive characteristic},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {8},
     year = {2020},
     doi = {10.1017/fms.2020.48},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.48/}
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Remy van Dobben de Bruyn; Matthias Paulsen. The construction problem for Hodge numbers modulo an integer in positive characteristic. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.48

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