Corpus ID: 223953370

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… Expand
2 Citations
Motivic Galois representations valued in Spin groups
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)Expand
Points on Shimura varieties modulo primes
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 theExpand

References

SHOWING 1-10 OF 106 REFERENCES
Deformations of Galois representations and exceptional monodromy
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 suchExpand
Automorphy and irreducibility of some l-adic representations
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 noExpand
The sign of Galois representations attached to automorphic forms for unitary groups
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 aExpand
On torsion in the cohomology of locally symmetric varieties
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 CMExpand
Galois representations for general symplectic groups
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields underExpand
On a lifting problem of L-packets
  • Bin Xu
  • Mathematics
  • Compositio 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 stillExpand
The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups of abelian type
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 typeExpand
Arithmetic invariants of discrete Langlands parameters
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 beExpand
Automorphy for some l-adic lifts of automorphic mod l Galois representations
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–TateExpand
Filtered F-crystals on Shimura varieties of abelian type
In this paper, we define and construct canonical filtered $F$-crystals with $G$-structure over the integral models for Shimura varieties of abelian type at hyperspecial level defined by Kisin. WeExpand
...
1
2
3
4
5
...