@article { ,
title = {The Breuil–Mézard conjecture when l≠p},
abstract = {Let l and p be primes, let F=Qp be a finite extension with absolute Galois group GF , let F be a finite field of characteristic l, and let W GF ! GLn.F/ be a continuous representation. Let R./ be the universal framed deformation ring for . If l D p, then the Breuil–Mézard conjecture (as recently formulated by Emerton and Gee) relates the mod l reduction of certain cycles in R./ to the mod l reduction of certain representations of GLn.OF /. We state an analogue of the Breuil–Mézard conjecture when l ¤ p, and we prove it whenever l>2 using automorphy lifting theorems. We give a local proof when l is “quasibanal” for F and is tamely ramified. We also analyze the reduction modulo l of the types . / defined by Schneider and Zink.},
doi = {10.1215/00127094-2017-0039},
eissn = {1547-7398},
issn = {0012-7094},
issue = {4},
journal = {Duke Mathematical Journal},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {603-678},
publicationstatus = {Published},
publisher = {Duke University Press},
url = {https://durham-repository.worktribe.com/output/1314057},
volume = {167},
year = {2018},
author = {Shotton, Jack}
}