REDUCTIONS of 2-DIMENSIONAL SEMISTABLE REPRESENTATIONS with LARGE L-INVARIANT

John Bergdall; Brandon Levin; Tong Liu

doi:10.1017/S1474748022000081

REDUCTIONS of 2-DIMENSIONAL SEMISTABLE REPRESENTATIONS with LARGE L-INVARIANT

John Bergdall, Brandon Levin, Tong Liu

Mathematics

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

Abstract

We determine reductions of 2-dimensional, irreducible, semistable, and non-crystalline representations of Gal(Q¯pQp)with Hodge-Tate weights 0 < k-1and with L-invariant whose p-adic norm is sufficiently large, depending on k. Our main result provides the first systematic examples of the reductions for k ≥p.

Original language	English (US)
Journal	Journal of the Institute of Mathematics of Jussieu
DOIs	https://doi.org/10.1017/S1474748022000081
State	Accepted/In press - 2022

Keywords

local Galois representations modulo p
p-adic Hodge theory
semistable representations

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S1474748022000081

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title = "REDUCTIONS of 2-DIMENSIONAL SEMISTABLE REPRESENTATIONS with LARGE L-INVARIANT",

abstract = "We determine reductions of 2-dimensional, irreducible, semistable, and non-crystalline representations of Gal(Q¯pQp)with Hodge-Tate weights 0 < k-1and with L-invariant whose p-adic norm is sufficiently large, depending on k. Our main result provides the first systematic examples of the reductions for k ≥p.",

keywords = "local Galois representations modulo p, p-adic Hodge theory, semistable representations",

author = "John Bergdall and Brandon Levin and Tong Liu",

note = "Funding Information: The first author was partially supported by an NSF Grant (DMS-1402005) and a Simons Collaboration Grant (#713782). The second author was supported by a grant from the Simons Foundation/SFARI (#585753). Publisher Copyright: {\textcopyright} The Author(s), 2022. Published by Cambridge University Press.",

year = "2022",

doi = "10.1017/S1474748022000081",

language = "English (US)",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - REDUCTIONS of 2-DIMENSIONAL SEMISTABLE REPRESENTATIONS with LARGE L-INVARIANT

AU - Bergdall, John

AU - Levin, Brandon

AU - Liu, Tong

N1 - Funding Information: The first author was partially supported by an NSF Grant (DMS-1402005) and a Simons Collaboration Grant (#713782). The second author was supported by a grant from the Simons Foundation/SFARI (#585753). Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press.

PY - 2022

Y1 - 2022

N2 - We determine reductions of 2-dimensional, irreducible, semistable, and non-crystalline representations of Gal(Q¯pQp)with Hodge-Tate weights 0 < k-1and with L-invariant whose p-adic norm is sufficiently large, depending on k. Our main result provides the first systematic examples of the reductions for k ≥p.

AB - We determine reductions of 2-dimensional, irreducible, semistable, and non-crystalline representations of Gal(Q¯pQp)with Hodge-Tate weights 0 < k-1and with L-invariant whose p-adic norm is sufficiently large, depending on k. Our main result provides the first systematic examples of the reductions for k ≥p.

KW - local Galois representations modulo p

KW - p-adic Hodge theory

KW - semistable representations

UR - http://www.scopus.com/inward/record.url?scp=85128470767&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85128470767&partnerID=8YFLogxK

U2 - 10.1017/S1474748022000081

DO - 10.1017/S1474748022000081

M3 - Article

AN - SCOPUS:85128470767

SN - 1474-7480

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

ER -

REDUCTIONS of 2-DIMENSIONAL SEMISTABLE REPRESENTATIONS with LARGE L-INVARIANT

Abstract

Keywords

ASJC Scopus subject areas

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