Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

In this thesis we build a Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo and Vigni built in towers of Shimura curves. We generalize the work of Buyukboduk to a quaternionic setting, relaxing the classical Heegner hypothesis on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families.