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There is no Definable Grauert Direct Image Theorem

Published 26 Jan 2026 in math.AG and math.LO | (2601.18711v1)

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.

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Authors (2)

  1. Hélène Esnault 
  2. Moritz Kerz 

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