There is no Definable Grauert Direct Image Theorem
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866914327308533760 |
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| author | Esnault, Hélène Kerz, Moritz |
| author_facet | Esnault, Hélène Kerz, Moritz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18711 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | There is no Definable Grauert Direct Image Theorem Esnault, Hélène Kerz, Moritz Algebraic Geometry Logic 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. |
| title | There is no Definable Grauert Direct Image Theorem |
| topic | Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2601.18711 |