The Lyndon–Demushkin method and crystallinelifts of G2-valued Galois representations

The Lyndon-Demushkin method and crystalline lifts of G 2 -valued Galois representations Zhongyipan LinWe develop obstruction theory for lifting characteristic-p local Galois representations valued in reductive groups of type B l , C l , D l or G 2 .An application of the Emerton-Gee stack then reduces the existence of crystalline lifts to a purely combinatorial problem when p is not too small.As a toy example, we show for all local fields K / p , with p > 3, all representations :, where G 2 is the exceptional Chevalley group of type G 2 .