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- Title
Companion forms in parallel weight one.
- Authors
Gee, Toby; Kassaei, Payman
- Abstract
Let $p\gt 2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a $\mathrm{mod} \hspace{0.167em} p$ Galois representation to arise from a $\mathrm{mod} \hspace{0.167em} p$ Hilbert modular form of parallel weight one, by proving a ‘companion forms’ theorem in this case. The techniques used are a mixture of modularity lifting theorems and geometric methods. As an application, we show that Serre’s conjecture for $F$ implies Artin’s conjecture for totally odd two-dimensional representations over $F$.
- Subjects
PRIME numbers; FORMALLY real fields; GALOIS theory; HILBERT modular surfaces; ARTIN'S conjecture
- Publication
Compositio Mathematica, 2013, Vol 149, Issue 6, p903
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X12000875