Potentially crystalline lifts of certain prescribed types

Toby Gee; Florian Herzig; Tong Liu; David Savitt

Potentially crystalline lifts of certain prescribed types

Toby Gee
, Florian Herzig
, Tong Liu
, David Savitt

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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: G_K → GL_n(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.

Original language	English (US)
Pages (from-to)	397-422
Number of pages	26
Journal	Documenta Mathematica
Volume	22
Issue number	2017
State	Published - 2017

ASJC Scopus subject areas

General Mathematics

Cite this

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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)",

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pages = "397--422",

journal = "Documenta Mathematica",

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T1 - Potentially crystalline lifts of certain prescribed types

AU - Gee, Toby

AU - Herzig, Florian

AU - Liu, Tong

AU - Savitt, David

N1 - 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

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85034428000

UR - https://www.scopus.com/pages/publications/85034428000#tab=citedBy

M3 - Article

AN - SCOPUS:85034428000

SN - 1431-0635

VL - 22

SP - 397

EP - 422

JO - Documenta Mathematica

JF - Documenta Mathematica

IS - 2017

ER -

Potentially crystalline lifts of certain prescribed types

Abstract

ASJC Scopus subject areas

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