This is a work in progress. Using recent works of Fukaya-Kato on Sharifi conjecture and of Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin on complete cohomology of modular curves, we construct an Euler system for universal deformation of rank two, which interpolates Kato's Eule r system for Galois representations associated to Hecke eigen cusp newforms.

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