Reciprocity laws for $({\phi }_L,{\mathrm{\Gamma }}_L)$-modules over Lubin-Tate extensions

In the Lubin-Tate setting we study pairings for analytic $({\phi }_L,{\mathrm{\Gamma }}_L)$-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.