On Perrin-Riou's exponential map for $(\phi ,\mathrm{\Gamma })$-modules

Let $K\mathrm{/}{\mathbb{Q}}_p$ be a finite Galois extension and $D$ a $(\varphi, \Gamma)$-moduleovertheRobba-ring$B^{\dagger}_{$\text{rig}$, K}$. We give a generalization of the Bloch-Kato exponential map for $D$ using continuous Galois-cohomology groups $H^i(G_K,W(D))$ for the $B$-pair $W(D)$ associated to $D$. We construct a big exponential map ${\mathrm{\Omega }}_{D,h}$ ($h\in \mathbb{N}$) for cyclotomic extensions of $K$ for $D$ in the style of Perrin-Riou using the theory of Berger’s $B$-pairs, which interpolates the generalized Bloch-Kato exponential maps on the finite levels.