학술논문
A Local Analogue of the Ghost Conjecture of Bergdall–Pollack
Document Type
Original Paper
Author
Source
Peking Mathematical Journal. 7(1):247-344
Subject
Language
English
ISSN
2096-6075
2524-7182
2524-7182
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.