Algebraic monodromy groups of $l$-adic representations of Gal$(\overline{\mathbb{Q}} /\mathbb{Q})$

@article{Tang2019AlgebraicMG,
  title={Algebraic monodromy groups of \$l\$-adic representations of Gal\$(\overline\{\mathbb\{Q\}\} /\mathbb\{Q\})\$},
  author={Shiang Tang},
  journal={Algebra \& Number Theory},
  year={2019},
  volume={13},
  pages={1353-1394}
}
  • Shiang Tang
  • Published 2019
  • Mathematics
  • Algebra & Number Theory
A connected reductive algebraic group $G$ is said to be an $l$-adic algebraic monodromy group for $\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q})$ if there is a continuous homomorphism $$\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q}) \to G(\overline{\mathbb Q}_l)$$ with Zariski-dense image. In this paper, we give a classification of connected $l$-adic algebraic monodromy groups for $\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q})$, in particular producing the first such examples for… Expand
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References

SHOWING 1-10 OF 37 REFERENCES
Galois representations with open image
We describe an approach to constructing Galois extensions of $${\mathbf{Q}}$$Q with Galois group isomorphic to an open subgroup of $$GL_n({\mathbf{Z}}_p)$$GLn(Zp) for various values of n and primesExpand
Motives with exceptional Galois groups and the inverse Galois problem
We construct motivic ℓ-adic representations of $\textup {Gal}(\overline {\mathbb{Q}}/\mathbb{Q})$ into exceptional groups of type E7,E8 and G2 whose image is Zariski dense. This answers a question ofExpand
Lifting of elements of Weyl groups
Suppose $G$ is a reductive algebraic group, $T$ is a Cartan subgroup, $N=\text{Norm}(T)$, and $W=N/T$ is the Weyl group. If $w\in W$ has order $d$, it is natural to ask about the orders lifts of $w$Expand
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
LIFTING GLOBAL REPRESENTATIONS WITH LOCAL PROPERTIES
Let k be a global field, with Galois group Gk and Weil group Wk relative to a choice of separable closure ks/k. Let Γ be either Gk or Wk, and H a linear algebraic group over F = C or Qp with p 6=Expand
Unobstructed modular deformation problems
<abstract abstract-type="TeX"><p>Let <i>f</i> be a newform of weight <i>k</i> ≥ 3 with Fourier coefficients in a number field <i>K</i>. We show that the universal deformation ring of the mod λ GaloisExpand
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
A note on Galois representations with big image
Given an integer N ≥ 3, we will first construct reasonably “motivic” representations ρ : Gal(Q/Q(ζN ))→ GL(n,Q`) with open image, for any ` which is 1 mod N and for certain n. We will do this inExpand
Topics in Galois Theory
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensionsExpand
Geometric Deformations of Orthogonal and Symplectic Galois Representations
For a representation over a finite field of characteristic p of the absolute Galois group of the rationals, we study the existence of a lift to characteristic zero that is geometric in the sense ofExpand
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