There is no Definable Grauert Direct Image Theorem
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Topology and Set Theory
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 January 2026
- Document type
- Preprint