Every mod p representation of the absolute Galois group of a p-adic local field lifts to a crystalline representation of regular Hodge-Tate weights, via the geometry of new moduli stacks of etale (phi,Gamma)-modules.
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Moduli stacks of \'etale (phi,Gamma)-modules and the existence of crystalline lifts
Every mod p representation of the absolute Galois group of a p-adic local field lifts to a crystalline representation of regular Hodge-Tate weights, via the geometry of new moduli stacks of etale (phi,Gamma)-modules.