  Let $K$ be a finite extension of $\mathbf{Q}_p$. We use the theory of
$(\varphi,\Gamma)$-modules in the Lubin-Tate setting to construct some
corestriction-compatible families of classes in the cohomology of $V$, for
certain representations $V$ of $\mathrm{Gal}(\overline{\mathbf{Q}}_p/K)$. If in
addition $V$ is crystalline, we describe these classes explicitly using
Bloch-Kato's exponential maps. This allows us to generalize Perrin-Riou's
period map to the Lubin-Tate setting.
