In my family, I especially thank my mother Paoline, my father Emerson, my stepfather Flaviano, my grandparents Álvaro and Euri and my girlfriend Débora, who offered support throughout my academic path and, thanks to them, I was able to take full advantage of the opportunities that were presented to me. I thank my advisor Nivaldo for receiving me as his student after a return to USP when I was struggling with my academic life and to present me situations outside my comfort zone that made me

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... I thank my professors Maria do Carmo Carbinatto and Leandro Fiorini Aurichi, for the exceptional role they played during my undergraduate years.In special I thank my friend Thales who, despite the distance generated by the pandemic, was always by my side diligently supporting my complaints. I thank CAPES for the financial support during the realization of this work. I thank the Eternal Blue Sky and the Fertile Mother Earth spirit for providing human life and the conditions that allow us to maintain it. Finally, I thank my sweet and lovely dog, Buddy, for being such a cheerful and playful companion, who showed me all the time that the best thing to do when our mind is tired and not working properly, then it is time to go for a walk. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001. "Above all, don't lie to yourself. The man who lies to himself and listens to his own lie comes to a point that he cannot distinguish the truth within him, or around him, and so loses all respect for himself and for others. And having no respect he ceases to love." ( Fyodor Dostoevsky, The Brothers Karamazov ) RESUMO TEZÔTO, I. T. O. Classes de Chern via formas diferenciais. 2022. 134 p. Dissertação (Mestrado em Ciências -