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Rigid-analytic varieties with projective reduction violating Hodge symmetry

Part of: Cycles and subschemes Abelian varieties and schemes Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  19 March 2021

Alexander Petrov
Alexander Petrov*
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA02138, [email protected]
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Abstract

We construct examples of smooth proper rigid-analytic varieties admitting formal models with projective special fibers and violating Hodge symmetry for cohomology in degrees ${\geq }3$. This answers negatively the question raised by Hansen and Li.

Keywords

rigid-analytic varietiesHodge symmetryp-adic Hodge theory

MSC classification

Primary: 14G20: Local ground fields
Secondary: 14G22: Rigid analytic geometry 14C30: Transcendental methods, Hodge theory , Hodge conjecture 14K22: Complex multiplication
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 3 , March 2021 , pp. 625 - 640
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Copyright
© The Author(s) 2021

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