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arXiv · 2001.02787

The Hodge ring of varieties in positive characteristic

Remy van Dobben de Bruyn
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Abstract

Let $k$ be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers $h^{i,j}(X) = \dim H^j(X,Ω_X^i)$ 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 $h^{i,0}(X)$ and the $h^{0,j}(X)$ (and their duals $h^{i,n}(X)$ and $h^{n,j}(X)$). The corresponding statements for compact Kähler manifolds were proven by Kotschick and Schreieder.

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BibTeXRIS

Remy van Dobben de Bruyn. 2020-01-09. The Hodge ring of varieties in positive characteristic. https://doi.org/10.2140/ant.2021.15.729

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