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2021 The Hodge ring of varieties in positive characteristic
Remy van Dobben de Bruyn
Algebra Number Theory 15(3): 729-745 (2021). DOI: 10.2140/ant.2021.15.729

Abstract

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.

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Remy van Dobben de Bruyn. "The Hodge ring of varieties in positive characteristic." Algebra Number Theory 15 (3) 729 - 745, 2021. https://doi.org/10.2140/ant.2021.15.729

Information

Received: 28 January 2020; Revised: 28 June 2020; Accepted: 7 September 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.729

Subjects:
Primary: 14G17
Secondary: 14A10 , 14E99 , 14F40 , 14F99

Keywords: Algebraic Geometry , birational invariants , de Rham cohomology , Grothendieck ring of varieties , Hodge cohomology , positive characteristic

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 3 • 2021
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