## Automorphic Galois representations and the inverse Galois problem for certain groups of type $D_{m}$

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- by Adrián Zenteno PDF
- Proc. Amer. Math. Soc.
**149**(2021), 89-95 Request permission

## Abstract:

Let $m$ be an integer greater than three and $\ell$ be an odd prime. In this paper we prove that at least one of the following groups: $\mathrm {P}\Omega ^\pm _{2m}(\mathbb {F}_{\ell ^s})$, $\mathrm {PSO}^\pm _{2m}(\mathbb {F}_{\ell ^s})$, $\mathrm {PO}_{2m}^\pm (\mathbb {F}_{\ell ^s})$, or $\mathrm {PGO}^\pm _{2m}(\mathbb {F}_{\ell ^s})$ is a Galois group of $\mathbb {Q}$ for infinitely many integers $s > 0$. This is achieved by making use of a slight modification of a group theory result of Khare, Larsen, and Savin, and previous results of the author on the images of the Galois representations attached to cuspidal automorphic representations of $\mathrm {GL}_{2m}(\mathbb {A}_\mathbb {Q})$.## References

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## Additional Information

**Adrián Zenteno**- Affiliation: Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile
- Email: adrian.zenteno@pucv.cl
- Received by editor(s): November 15, 2019
- Received by editor(s) in revised form: May 18, 2020, and May 31, 2020
- Published electronically: October 20, 2020
- Additional Notes: The author was supported by CONICYT Proyecto FONDECYT Postdoctorado No. 3190474.
- Communicated by: Romyar Sharifi
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 89-95 - MSC (2010): Primary 11F80; Secondary 12F12, 20G40
- DOI: https://doi.org/10.1090/proc/15253
- MathSciNet review: 4172588