Using the theory of (ϕ, Γ)-modules we generalize Greenberg's construction of the L-invariant to p-adic representations which are semistable at p.

Résumé. Soit K une extension finie non-ramifiée de Q p et V une représentation cristalline de Gal(Q p /K). Dans cet article, on montre la conjecture Abstract. Let K be a finite unramified extension of Q p and let V be a crystalline representation of Gal(Q p /K). In this article, we give a proof of theThe main ingredients are the δ Z p (V ) conjecture about the integrality of Perrin-Riou's exponential, which we prove using the theory of (ϕ, )-modules, and Iwasawa-theoretic descent techniques used to show that

No abstract

Abstract. We formulate a conjecture about extra zeros of p-adic L-functions at near central points which generalizes the conjecture formulated in [Ben2]. We prove that this conjecture is compatible with Perrin-Riou's theory of p-adic L-functions. Namely, using Nekovář's machinery of Selmer complexes we prove that our L -invariant appears as an additional factor in the Bloch-Kato type formula for special values of Perrin-Riou's module of L-functions.