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Crystalline Lifts of G-Valued Galois Representations with Fixed Abelianization

An existence result in p-adic Hodge theory: every quasi-semisimple mod-p Galois representation valued in a reductive group G admits a crystalline lift with regular Hodge-Tate weights whose abelianization equals a prescribed crystalline lift of the original abelianization, with an analogue for L-parameters of quasi-split tame groups via the Langlands dual group.

Demerzel Text

2501.00259

This number-theory paper proves the existence of crystalline lifts of continuous quasi-semisimple mod-p G-valued Galois representations of the absolute Galois group of a p-adic field K, for a split r…