Duke Mathematical Journal

Base change and a problem of Serre

C. M. Skinner and A. J. Wiles

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We establish a version of "level-lowering" for mod p Galois representations arising from the reductions of representations associated to Hilbert modular forms. In particular, we show that level-lowering can be easily achieved if one replaces the base field with a suitable solvable extension. This is often enough for applications to proving the modularity of p-adic representations.

Article information

Duke Math. J., Volume 107, Number 1 (2001), 15-25.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F80: Galois representations
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]


Skinner, C. M.; Wiles, A. J. Base change and a problem of Serre. Duke Math. J. 107 (2001), no. 1, 15--25. doi:10.1215/S0012-7094-01-10712-6. https://projecteuclid.org/euclid.dmj/1091736134

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  • \lccH. Carayol, Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986), 409–468.
  • \lccP. Deligne, Formes modulaires et représentations de $\ell$-adiques, Seminaire Bourbaki, 1969, exp. no. 355, Lecture Notes in Math. 179, Springer, Berlin, 1971, 139–172.
  • \lccF. Diamond, “The refined conjecture of Serre” in Elliptic Curves, Modular Forms, and Fermat's Last Theorem (Hong Kong, 1993), Internat. Press, Cambridge, Mass., 1995, 22–37.
  • \lccK. Fujiwara, Deformation rings and Hecke rings in the totally real case, preprint.
  • \lccF. Jarvis, Level lowering for modular mod $\ell$ representations over totally real fields, Math. Ann. 313 (1999), 141–160.
  • \lccA. Rajaei, On lowering the levels in modular mod $\ell$ Galois representations of totally real fields, Ph.D. dissertation, Princeton Univ., Princeton, 1998.
  • \lccK. Ribet, On modular representations of $\Gal (\overline{\bold Q}/\bold Q)$ arising from modular forms, Invent. Math. 100 (1990), 431–476.
  • \lccJ.-P. Serre, Sur les représentations modulaires de degré $2$ de $\Gal(\overline{\bold Q}/\bold Q)$, Duke Math. J. 54 (1987), 179–230.
  • \lccG. Shimura, Introduction to the Arithmetic Theory of Automorphic Forms, Kanô Memorial Lectures 1, Iwanami Shoten, Tokyo, Publ. Math. Soc. Japan 11, Princeton Univ. Press, Princeton, 1971.
  • \lccC. Skinner \and A. Wiles, Residually reducible representations and modular forms, Inst. Hautes Études Sci. Publ. Math. 89 (1999), 5–126.
  • ––––, Nearly ordinary deformations of irreducible residual representations, preprint, 1998.
  • \lccR. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), 265–280.
  • \lccA. Wiles, On ordinary $\lambda$-adic representations associated to modular forms, Invent. Math. 94 (1988), 529–573.
  • ––––, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), 443–551.