Perrin-Riou, Bernadette \(p\)-adic \(L\)-functions and \(p\)-adic representations. Transl. from the French by Leila Schneps. (English) Zbl 0988.11055 SMF/AMS Texts and Monographs. 3. Providence, RI: American Mathematical Society (AMS). xx, 150 p. (2000). The present text is essentially an English translation of the French original [Astérisque 229, Paris, SMF (1995; Zbl 0845.11040)] with a few corrections and small improvements. A short Addendum points out some progress that has been made since the French version appeared. In particular, the reciprocity law Rec(\(V\)), which appeared as a hypothesis for some theorems in the original, has now been proved by P. Colmez [Ann. Math. (2) 148, 485-571 (1998; Zbl 0928.11045)]. Reviewer: Lawrence Washington (College Park) Cited in 1 ReviewCited in 25 Documents MSC: 11R42 Zeta functions and \(L\)-functions of number fields 11R23 Iwasawa theory 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11G45 Geometric class field theory 11F33 Congruences for modular and \(p\)-adic modular forms 11S25 Galois cohomology Keywords:\(p\)-adic \(L\)-functions; \(p\)-adic representations; Iwasawa theory; Galois cohomology Citations:Zbl 0928.11045; Zbl 0845.11040 PDFBibTeX XMLCite \textit{B. Perrin-Riou}, \(p\)-adic \(L\)-functions and \(p\)-adic representations. Transl. from the French by Leila Schneps. Providence, RI: American Mathematical Society (AMS) (2000; Zbl 0988.11055)