We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge-Tate weights and inertial types of a given representation , where is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, making use of automorphy lifting theorems.
Cite this article
Toby Gee, Florian Herzig, Tong Liu, David Savitt, Potentially Crystalline Lifts of Certain Prescribed Types. Doc. Math. 22 (2017), pp. 397–422DOI 10.4171/DM/569