@article{d50b4a8892244bd3a91f1bf4ed9f399d,
title = "Potentially crystalline lifts of certain prescribed types",
abstract = "We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge-Tate weights and inertial types of a given representation r: GK → GLn(Fp), where K/Qp 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.",
author = "Toby Gee and Florian Herzig and Tong Liu and David Savitt",
note = "Funding Information: 1The first author was partially supported by a Leverhulme Prize, EPSRC grant EP/L025485/1, Marie Curie Career Integration Grant 303605, and by ERC Starting Grant 306326. The second author was partially supported by a Sloan Fellowship and an NSERC grant The third author was partially supported by NSF grants DMS-0901360 and DMS-1406926 The fourth author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032",
year = "2017",
language = "English (US)",
volume = "22",
pages = "397--422",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "European Mathematical Society Publishing House",
number = "2017",
}