The Hodge conjecture is difficult because sophisticated submanifolds are certainly rigid objects (considering the fact that they are defined by polynomials). Actually, it is very hard to build sophisticated submanifolds, and you can find not many of these. Proving that submanifolds exist with no developing them (a very beneficial type https://socialbuzztoday.com/story4748860/new-step-by-step-map-for-bos138