A Conditional Proof of the Hodge Conjecture
Year: 2025
Type: article
Abstract: This work presents an unconditional proof of the Hodge Conjecture. Unlike previous approaches that rely on conditional assumptions such as the standard conjectures or semisimplicity hypotheses, this proof is developed without any such prerequisites. All logical steps, constructions, and arguments have been formulated to avoid reliance on unproven conjectures, thereby providing a fully unconditional resolution to the conjecture. Detailed constructions of absolute Hodge classes, monodromy arguments, and explicit algebraic cycle realizations are included to ensure the completeness and rigor of the proof.
Author: Lee, Donghyun
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6968438239
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