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The Hodge ring of varieties in positive characteristic
Algebra & Number Theory  (IF0.938),  Pub Date : 2021-05-20, DOI: 10.2140/ant.2021.15.729
Remy van Dobben de Bruyn

Let k be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers hi,j(X) = dimHj(X,ΩXi) that hold for every smooth proper variety X over k are the ones given by Serre duality. We also show that the only linear combinations of Hodge numbers that are birational invariants of X are given by the span of the hi,0(X) and the h0,j(X) (and their duals hi,n(X) and hn,j(X)). The corresponding statements for compact Kähler manifolds were proven by Kotschick and Schreieder.