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arXiv · 2601.18711

There is no Definable Grauert Direct Image Theorem

Hélène Esnault·Moritz Kerz
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Abstract

We prove the claim in the title by showing that a definable Grauert Direct Image Theorem in o-minimal geometry would imply a weak representability-like property of the definable Picard functor. However, this weak representability cannot hold because of the Definable Chow Theorem of Peterzil and Starchenko. v2: small typos corrected.

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Hélène Esnault, Moritz Kerz. 2026-01-26. There is no Definable Grauert Direct Image Theorem. https://arxiv.org/abs/2601.18711

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