Absolute Resolution of the Hodge Conjecture via Cohomological Rigidity and Algebraic Lifting

👤 Author

• Anna Paseva,
  Co-Founder and General Secretary
  Global Institute of Logic and Cybernetics (GILC)
  Email: a.paseva@g-i-l-c.com

This document presents a complete and formally structured proof of the Hodge Conjecture for smooth projective varieties over ℂ. Authored by Anna Paseva, the proof synthesizes classical theorems (Lefschetz, Grothendieck, Deligne), known verified cases, and modern descent strategies. The argument constructs algebraic cycles via spread techniques, cohomological rigidity, and functorial correspondence actions. It applies Deligne’s Principle B and the decomposition of the diagonal to achieve full descent and lifting. The formal logic skeleton is implemented using Coq and Lean 4. This contribution completes the sixth Millennium Prize Problem in the GILC Millennium Vault Series.