Reciprocity Laws for $({\phi }_L,{\Gamma }_L)$-Modules over Lubin–Tate Extensions

In the Lubin–Tate setting we study pairings for analytic $({\phi }_L,{\Gamma }_L)$-modules and prove an abstract reciprocity law which then implies a relation between the analogue of Perrin-Riou's big exponential map as developed by Berger and Fourquaux and a $p$-adic regulator map whose construction relies on the theory of Kisin–Ren modules generalising the concept of Wach modules to the Lubin–Tate situation.