## Duke Mathematical Journal

### Base change and a problem of Serre

#### Abstract

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

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

Dates
First available in Project Euclid: 5 August 2004

https://projecteuclid.org/euclid.dmj/1091736134

Digital Object Identifier
doi:10.1215/S0012-7094-01-10712-6

Mathematical Reviews number (MathSciNet)
MR1815248

Zentralblatt MATH identifier
1016.11017

#### Citation

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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