Complete Unconditional Resolution of the Hodge Conjecture via Classical Analytic and Arithmetic Methods
Year: 2025
Type: article
Abstract: We establish an unconditional, purely classical resolution of the Hodge Conjecture within the Discrete Regulator (DR)–REFP framework. All analytic and arithmetic components are proved using classical Hodge theory, Demailly-type regularization of Green currents, Bochner–Kodaira identities on primitive pieces, and Arakelov comparison on semistable models, without relying on Ricci or Kähler–Ricci flow. This manuscript supersedes and completes the conceptual program initiated in the earlier preprint “Conjectura de Hodge (1)”, which is cited as philosophical background; the present paper is self-contained and provides the full technical closure. The proof establishes that every rational Hodge class on any smooth projective variety is algebraic, completing one of the seven Clay Millennium Prize Problems.
Author: Rodrigues, Vinicius Ramos
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7104376605
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