Deformations of Galois representations and exceptional monodromy

Abstract

For any simple algebraic group $G$ of exceptional type, we construct geometric $\ell$-adic Galois representations with algebraic monodromy group equal to $G$, in particular producing the first such examples in types ${\mathrm{F}}_4$ and ${\mathrm{E}}_6$. To do this, we extend to general reductive groups Ravi Ramakrishna's techniques for lifting odd two-dimensional Galois representations to geometric $\ell$-adic representations.

Cited by in corpus (14)

• G-valued local deformation rings and global lifts
• Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations
• Lifting irreducible Galois representations
• Algebraic monodromy groups of $l$-adic representations of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$
• Quantitative level lowering for Galois representations
• Potential automorphy of ${\mathrm{GSpin}}_{2n+1}$-valued Galois representations
• Liftable groups, negligible cohomology and Heisenberg representations
• Galois representations for even general special orthogonal groups
• Deformations of Certain Reducible Galois Representations, III
• Compatible systems of Galois representations associated to the exceptional group E6
• Density of Selmer ranks in families of even Galois representations, Wiles' formula, and global reciprocity
• Motivic Galois representations valued in Spin groups
• A Refined Lifting Theorem for Supersingular Galois Representations
• Deformations of Reducible Galois Representations to Hida-Families