Corpus ID: 203902471

Potential automorphy of $\mathrm{GSpin}_{2n+1}$-valued Galois representations

  title={Potential automorphy of \$\mathrm\{GSpin\}\_\{2n+1\}\$-valued Galois representations},
  author={Stefan Patrikis and Shiang Tang},
  journal={arXiv: Number Theory},
We prove a potentially automorphy theorem for suitable Galois representations $\Gamma_{F^+} \to \mathrm{GSpin}_{2n+1}(\overline{\mathbb{F}}_p)$ and $\Gamma_{F^+} \to \mathrm{GSpin}_{2n+1}(\overline{\mathbb{Q}}_p)$, where $\Gamma_{F^+}$ is the absolute Galois group of a totally real field $F^+$. We also prove results on solvable descent for $\mathrm{GSp}_{2n}(\mathbb{A}_{F^+})$ and use these to put representations $\Gamma_{F^+} \to \mathrm{GSpin}_{2n+1}(\overline{\mathbb{Q}}_p)$ into compatible… Expand
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