AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Peking Mathematical Journal Article
Article Link
Cite
EndNote(RIS) BibTeX
Collect
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Original Article

A Local Analogue of the Ghost Conjecture of Bergdall–Pollack

School of Mathematical Sciences, Peking University, 5 Yi He Yuan Road, Haidian District, Beijing 100871, China
Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, HI 96822, USA
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Show Author Information

Abstract

We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL2(Qp). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.

Keywords

EigencurvesSlope of Up operatorsOverconvergent modular formsCompleted cohomologyWeight spaceGouvêa’s conjectureGouvêa–Mazur conjecture
Peking Mathematical Journal
Volume 7 Issue 1,
March 2024
Pages 247-344
DOI: 10.1007/s42543-023-00063-7
Cite this article:
Liu, R., Truong, N.X., Xiao, L. et al. A Local Analogue of the Ghost Conjecture of Bergdall–Pollack. Peking Math J 7, 247-344 (2024). https://doi.org/10.1007/s42543-023-00063-7

113

Views

2

Crossref

Altmetrics
Received: 11 December 2021
Revised: 30 October 2022
Accepted: 14 February 2023
Published: 02 August 2023
© Peking University 2023
Return