Hida, H.; Tilouine, J. Katz \(p\)-adic \(L\)-functions, congruence modules and deformation of Galois representations. (English) Zbl 0739.11022 \(L\)-functions and arithmetic, Proc. Symp., Durham/UK 1989, Lond. Math. Soc. Lect. Note Ser. 153, 271-293 (1991). [For the entire collection see Zbl 0718.00005.]The authors generalize results of Mazur and Tilouine giving a proof of the anticyclotomic main conjecture. More precisely, they prove a generalization, to the \(CM\) case, of certain divisibility relations (predicted by the main conjecture) between a Katz \(p\)-adic \(L\)-function and certain characteristic power series. They also re-prove some of the divisibility results of Mazur-Tilouine without the additional hypotheses needed in the original proof. The proof uses the theory of deformations of Galois representations over finite extensions of \(\mathbb{Q}_ p\). Reviewer: S.Kamienny (Los Angeles) Cited in 1 ReviewCited in 9 Documents MSC: 11F85 \(p\)-adic theory, local fields 11R23 Iwasawa theory 11S40 Zeta functions and \(L\)-functions 11F80 Galois representations 11G15 Complex multiplication and moduli of abelian varieties 11R32 Galois theory Keywords:CM field; anticyclotomic main conjecture; divisibility relations; Katz \(p\)-adic \(L\)-function; power series; deformations of Galois representations Citations:Zbl 0718.00005 PDF BibTeX XML Cite \textit{H. Hida} and \textit{J. Tilouine}, Lond. Math. Soc. Lect. Note Ser. None, 271--293 (1991; Zbl 0739.11022) OpenURL