Zero-Defect Algebraization from First Principles: A Complete Unconditional Closure of the Hodge Conjecture
Abstract
Let X be a smooth complex projective variety and let Hdg?(X) = H²?(X, ?) ? H?,?(X, ?) denote the space of rational Hodge classes of codimension p. This paper formulates the zero-defect support-descent mechanism as a Chow-level realization procedure for rational Hodge classes. André’s motivated-cycle theorem places every class ? ? Hdg?(X) inside a finite support presentation whose edges consist of algebraic correspondences, pull-backs, push-forwards, cup-products with divisor classes, and inverse Lefschetz operators. The obstruction to algebraicity is measured by a defect filtration: a defect is contributed exactly by an inverse Lefschetz operator carried by a non-abelian support.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- International Journal of Inventions in Engineering & Science Technology
- Publisher
- IJRSSH Publication
- Volume
- 12
- Issue
- 1
- Pages
- 72–113
- Publication date
- 1 January 2026
- Language
- EN