# Galois representations for even general special orthogonal groups

@article{Kret2020GaloisRF, title={Galois representations for even general special orthogonal groups}, author={Arno Kret and Sug Woo Shin}, journal={arXiv: Number Theory}, year={2020} }

We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type $D^{\mathbb{H}}$, arising from forms of $\mathrm{GSO}_{2n}$. As an application…

## 2 Citations

### Motivic Galois representations valued in Spin groups

- Mathematics
- 2020

Let $m$ be an integer such that $m \geq 7$ and $m \equiv 0,1,7 \mod 8$. We construct strictly compatible systems of representations of $\Gamma_{\mathbb Q} \to \mathrm{Spin}_m(\overline{\mathbb Q}_l)…

### Points on Shimura varieties modulo primes

- Mathematics
- 2021

We survey recent developments on the Langlands–Rapoport conjecture for Shimura varieties modulo primes and an analogous conjecture for Igusa varieties. We discuss resulting implications on the…

## References

SHOWING 1-10 OF 96 REFERENCES

### Deformations of Galois representations and exceptional monodromy

- Mathematics
- 2015

For any simple algebraic group G of exceptional type, we construct geometric $$\ell $$ℓ-adic Galois representations with algebraic monodromy group equal to G, in particular producing the first such…

### Automorphy and irreducibility of some l-adic representations

- MathematicsCompositio Mathematica
- 2014

Abstract In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no…

### The sign of Galois representations attached to automorphic forms for unitary groups

- MathematicsCompositio Mathematica
- 2011

Abstract Let K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a…

### On torsion in the cohomology of locally symmetric varieties

- Mathematics
- 2013

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM…

### Galois representations for general symplectic groups

- MathematicsJournal of the European Mathematical Society
- 2022

We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under…

### Geometrization of the local Langlands correspondence

- Mathematics
- 2016

Following the idea of [Far16], we develop the foundations of the geometric Langlands program on the Fargues--Fontaine curve. In particular, we define a category of $\ell$-adic sheaves on the stack…

### On a lifting problem of L-packets

- MathematicsCompositio Mathematica
- 2016

Let $G\subseteq \widetilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and having the same derived group. Although the existence of L-packets is still…

### The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups of abelian type

- Mathematics
- 2019

Author(s): Youcis, Alexander Frank | Advisor(s): Shin, Sug Woo | Abstract: In \cite{ScholzeDeformation} Scholze describes a formula, similar to those classically known as Langlands-Kottwitz type…

### Arithmetic invariants of discrete Langlands parameters

- Mathematics
- 2010

Let G be a reductive algebraic group over the local field k. The local Langlands conjecture predicts that the irreducible complex representations π of the locally compact group G(k) can be…

### Automorphy for some l-adic lifts of automorphic mod l Galois representations

- Mathematics
- 2008

We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate…