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

Abstract

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.

149 pages