  Let $K$ be a finite unramified extension of $\Qp$ and let $V$ be a
crystalline representation of $\mathrm{Gal}(\Qpbar/K)$. In this article, we
give a proof of the $C_{\mathrm{EP}}(L,V)$ conjecture for $L \subset
\Qp^{\mathrm{ab}}$ as well as a proof of its equivariant version
$C_{\mathrm{EP}}(L/K,V)$ for $L \subset \cup_{n=1}^\infty K(\zeta_{p^n})$. The
main ingredients are the $\delta_{\Zp}(V)$ conjecture about the integrality of
Perrin-Riou's exponential, which we prove using the theory of
$(\phi,\Gamma)$-modules, and Iwasawa-theoretic descent techniques used to show
that $\delta_{\Zp}(V)$ implies $C_{\mathrm{EP}}(L/K,V)$.
