In this talk, we'll present a construction of Z_p^Syn, a derived stack on p-adic formal bounded schemes which "geometrifies the crystalline condition from p-adic Hodge theory", which is amenable to discussing its moduli of (deformations of) perfect complexes and utilizing results from algebraic K-theory. We'll then describe some structures and invariants on such moduli related to Iwasawa Main Conjectures with an emphasis on the connections with parallel constructions in low-dimensional topology settings.