Reciprocity laws for $(\varphi_L,\Gamma_L)$-modules over Lubin-Tate extensions

TL;DR

This paper establishes reciprocity laws for $(phi_L,Gamma_L)$-modules over Lubin-Tate extensions, linking exponential and regulator maps in $p$-adic Hodge theory.

Contribution

It introduces an abstract reciprocity law in the Lubin-Tate setting, connecting Perrin-Riou's exponential map with $p$-adic regulator maps via Kisin-Ren modules.

Findings

Proves an abstract reciprocity law for $(phi_L,Gamma_L)$-modules.

Relates exponential maps to $p$-adic regulator maps in Lubin-Tate extensions.

Generalizes Wach modules using Kisin-Ren modules in this context.

Abstract

In the Lubin-Tate setting we study pairings for analytic $(\varphi_L,\Gamma_L)$-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.