Potentially Crystalline Lifts of Certain Prescribed Types

Toby Gee; Florian Herzig; Tong Liu; David Savitt

doi:10.4171/dm/569

JournalsdmVol. 22pp. 397–422

Potentially Crystalline Lifts of Certain Prescribed Types

Toby Gee
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Florian Herzig
Department of Mathematics, University of Toronto, Canada
Tong Liu
Department of Mathematics, Purdue University, USA
David Savitt
Department of Mathematics, Johns Hopkins University

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Abstract

We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge-Tate weights and inertial types of a given representation $\overline{r} : G_{K} \to GL_{n} (\overline{F}_{p})$ , where $K / Q_{p}$ 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.

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Toby Gee, Florian Herzig, Tong Liu, David Savitt, Potentially Crystalline Lifts of Certain Prescribed Types. Doc. Math. 22 (2017), pp. 397–422

DOI 10.4171/DM/569