A Deformation Theoretic Reduction of the Hodge Conjecture via Derived Categories and Complete Intersections
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908489249456128 |
|---|---|
| author | Mansour, Karim |
| author_facet | Mansour, Karim |
| contents | We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture unconditionally in the complete intersection case using derived category methods. Through deformation arguments, we reduce the general case to the algebraicity of limits. While this remains an assumption, our framework unifies Hodge theory, deformation, and derived techniques, offering a concrete path toward resolving the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Deformation Theoretic Reduction of the Hodge Conjecture via Derived Categories and Complete Intersections Mansour, Karim Algebraic Geometry We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture unconditionally in the complete intersection case using derived category methods. Through deformation arguments, we reduce the general case to the algebraicity of limits. While this remains an assumption, our framework unifies Hodge theory, deformation, and derived techniques, offering a concrete path toward resolving the conjecture. |
| title | A Deformation Theoretic Reduction of the Hodge Conjecture via Derived Categories and Complete Intersections |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.09934 |