A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Companion forms in parallel weight one
2013
Compositio Mathematica
Preserved Fulltext
Other Versions
AbstractLet$p\gt 2$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
doi:10.1112/s0010437x12000875
fatcat:r4gna72ovbgnxl5bveafia3njy