Ribet, Kenneth A. Images of semistable Galois representations. Special issue of the Pacific Journal of Mathematics. (English) Zbl 0942.11032 Aschbacher, Michael (ed.) et al., Olga Taussky-Todd: In memoriam. Cambridge, MA: International Press. Pac. J. Math., Spec. Issue, 277-297 (1998). The author considers 2-dimensional irreducible mod \(p\) Galois representations \(\rho\) of the Galois group of \(\mathbb{Q}\) that are “semistable”. In this article the image of such representations is shown to be as large as possible (at least for \(p>3\)). This is then applied to studying mod \(p\) and \(p\)-adic representations arising from \(J_0(N)\), the latter under an assumption that \(p\) is unramified in the corresponding Hecke algebra. In a recent work the author has been able to ameliorate this condition.For the entire collection see [Zbl 0889.00012]. Reviewer: Chandrashekhar B.Khare (Mumbai) Cited in 12 Documents MSC: 11F80 Galois representations Keywords:irreducible \(\text{mod }p\) Galois representations; semistable; \(p\)-adic representations; Hecke algebra PDFBibTeX XMLCite \textit{K. A. Ribet}, in: Olga Taussky-Todd: In memoriam. Cambridge, MA: International Press. Pac. J. Math., Spec. Issue, 277--297 (1998; Zbl 0942.11032)