Deformations of Galois representations and exceptional monodromy

摘要

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