Constructing Galois Representations with Very Large Image
Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 208-221

Voir la notice de l'article provenant de la source Cambridge University Press

Starting with a 2-dimensional mod $p$ Galois representation, we construct a deformation to a power series ring in infinitely many variables over the $p$ -adics. The image of this representation is full in the sense that it contains $S{{L}_{2}}$ of this power series ring. Furthermore, all ${{\mathbb{Z}}_{p}}$ specializations of this deformation are potentially semistable at $p$ .
DOI : 10.4153/CJM-2008-009-7
Mots-clés : 11F80, Galois representation, deformation.
Ramakrishna, Ravi. Constructing Galois Representations with Very Large Image. Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 208-221. doi: 10.4153/CJM-2008-009-7
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[B] Böckle, G., A local-to-global principle for deformations of Galois representations. J. Reine Angew. Math. 509(1999), 199–236. Google Scholar

[Bo] Boston, N., Appendix to On p-adic families of Galois representations, by A. Wiles and B. Mazur. Compositio Math. 59(1986), no. 2, 261–264. Google Scholar

[KLR1] Khare, C., Larsen, M., and Ramakrishna, R., Constructing semisimple p-adic Galois representations with prescribed properties. Amer. J. Math. 127(2005), no. 4, 709–734. Google Scholar

[KLR2] Khare, C., Transcendental ℓ-adic Galois representations. Math Res. Let. (2005), no. 5-6, 685–699. Google Scholar

[M1] Mazur, B., Deforming Galois representations. In: Galois Groups over Q. Math. Sci. Res. Inst. Publ. 16, Springer-Verlag, Berlin, 1989. Google Scholar

[M2] Mazur, B., An introduction to the deformation theory of Galois representations. In: Modular Forms and Fermat's Last Theorem. Springer, New York, 1997, pp. 243–311. Google Scholar

[NSW] Neukirch, J., Schmidt, A., and Wingberg, K., Cohomology of number fields, Grundlehren der MathematischenWissenschaften 323, Springer-Verlag, 2000. Google Scholar

[R1] Ramakrishna, R., Lifting Galois representations. Invent.Math. 138(1999), no. 3, 537–562. Google Scholar

[R2] Ramakrishna, R., Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur. Ann. of Math. 156(2002), no. 1, 115–154. Google Scholar

[Ro1] Rohrlich, D., False division towers of elliptic curves. J. Algebra 229(2000), no. 1, 249–279. Google Scholar

[Ro2] Rohrlich, D., Modular units and the surjectivity of a Galois representation. J. Number Theory 107(2004), no. 1, 8–24. Google Scholar

[T] Taylor, R., On icosahedral Artin representations. II. Amer. J. Math. 125(2003), no. 3, 549–566. Google Scholar

[W] Wiles, A., Modular elliptic curves and Fermat's last theorem. Ann. of Math. 141(1995), no. 3, 443–551. Google Scholar

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