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arXiv · 1507.01294

Deformations of Galois representations and exceptional monodromy

Stefan Patrikis
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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.

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Stefan Patrikis. 2015-07-05. Deformations of Galois representations and exceptional monodromy. https://doi.org/10.1007/s00222-015-0635-3

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