The eigencurve is proper

Hansheng Diao; Ruochuan Liu

doi:10.1215/00127094-3450536

The eigencurve is proper

Hansheng Diao, Ruochuan Liu

Mathematics

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

9 Scopus citations

Abstract

We prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion for properness introduced by Buzzard and Calegari. This gives a negative answer to a question of Coleman and Mazur.

Original language	English (US)
Pages (from-to)	1381-1395
Number of pages	15
Journal	Duke Mathematical Journal
Volume	165
Issue number	7
DOIs	https://doi.org/10.1215/00127094-3450536
State	Published - May 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-3450536

Cite this

@article{6f814488e2064f119981773f485d9d7c,

title = "The eigencurve is proper",

abstract = "We prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion for properness introduced by Buzzard and Calegari. This gives a negative answer to a question of Coleman and Mazur.",

author = "Hansheng Diao and Ruochuan Liu",

note = "Publisher Copyright: {\textcopyright} 2016.",

year = "2016",

month = may,

day = "1",

doi = "10.1215/00127094-3450536",

language = "English (US)",

volume = "165",

pages = "1381--1395",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "7",

}

TY - JOUR

T1 - The eigencurve is proper

AU - Diao, Hansheng

AU - Liu, Ruochuan

PY - 2016/5/1

Y1 - 2016/5/1

N2 - We prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion for properness introduced by Buzzard and Calegari. This gives a negative answer to a question of Coleman and Mazur.

AB - We prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion for properness introduced by Buzzard and Calegari. This gives a negative answer to a question of Coleman and Mazur.

UR - http://www.scopus.com/inward/record.url?scp=84971236564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971236564&partnerID=8YFLogxK

U2 - 10.1215/00127094-3450536

DO - 10.1215/00127094-3450536

M3 - Article

AN - SCOPUS:84971236564

SN - 0012-7094

VL - 165

SP - 1381

EP - 1395

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 7

ER -

The eigencurve is proper

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this