General Serre weight conjectures

Toby Gee; Florian Herzig; David Savitt

doi:10.4171/JEMS/826

General Serre weight conjectures

Toby Gee, Florian Herzig, David Savitt

Mathematics

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

30 Scopus citations

Abstract

We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL_n over an arbitrary number field, motivated by the formalism of the Breuil-Mézard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Q_p, and we also generalise the second author's previous conjecture for GL_n/Q to this setting, and show that the two conjectures are generically in agreement.

Original language	English (US)
Pages (from-to)	2859-2949
Number of pages	91
Journal	Journal of the European Mathematical Society
Volume	20
Issue number	12
DOIs	https://doi.org/10.4171/JEMS/826
State	Published - 2018

Keywords

Automorphic representations
Breuil-Mézard conjecture
Crystalline representations
Galois representations
L-parameters
Mod p Langlands correspondence
Patching functors
Serre weight
Serre's conjecture

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.4171/JEMS/826

Cite this

@article{b0246eb2f2e24668a710af796a89a6ea,

title = "General Serre weight conjectures",

abstract = "We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil-M{\'e}zard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Qp, and we also generalise the second author's previous conjecture for GLn/Q to this setting, and show that the two conjectures are generically in agreement.",

keywords = "Automorphic representations, Breuil-M{\'e}zard conjecture, Crystalline representations, Galois representations, L-parameters, Mod p Langlands correspondence, Patching functors, Serre weight, Serre's conjecture",

author = "Toby Gee and Florian Herzig and David Savitt",

note = "Funding Information: The 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. Funding Information: The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032. Funding Information: The second author was partially supported by NSF grants DMS-0902044 and DMS-0932078, a Sloan Fellowship, and an NSERC grant. Publisher Copyright: {\textcopyright} European Mathematical Society 2018",

year = "2018",

doi = "10.4171/JEMS/826",

language = "English (US)",

volume = "20",

pages = "2859--2949",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "12",

}

TY - JOUR

T1 - General Serre weight conjectures

AU - Gee, Toby

AU - Herzig, Florian

AU - Savitt, David

N1 - Funding Information: The 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. Funding Information: The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032. Funding Information: The second author was partially supported by NSF grants DMS-0902044 and DMS-0932078, a Sloan Fellowship, and an NSERC grant. Publisher Copyright: © European Mathematical Society 2018

PY - 2018

Y1 - 2018

N2 - We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil-Mézard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Qp, and we also generalise the second author's previous conjecture for GLn/Q to this setting, and show that the two conjectures are generically in agreement.

AB - We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil-Mézard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Qp, and we also generalise the second author's previous conjecture for GLn/Q to this setting, and show that the two conjectures are generically in agreement.

KW - Automorphic representations

KW - Breuil-Mézard conjecture

KW - Crystalline representations

KW - Galois representations

KW - L-parameters

KW - Mod p Langlands correspondence

KW - Patching functors

KW - Serre weight

KW - Serre's conjecture

UR - http://www.scopus.com/inward/record.url?scp=85048483607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048483607&partnerID=8YFLogxK

U2 - 10.4171/JEMS/826

DO - 10.4171/JEMS/826

M3 - Article

AN - SCOPUS:85048483607

SN - 1435-9855

VL - 20

SP - 2859

EP - 2949

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 12

ER -

General Serre weight conjectures

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this