A Local Analogue of the Ghost Conjecture of Bergdall-Pollack  

作　　者：Ruochuan Liu Nha Xuan Truong Liang Xiao Bin Zhao 

机构地区：[1]School of Mathematical Sciences,Peking University,5 Yi He Yuan Road,Haidian District,Beijing 100871,China [2]Department of Mathematics,University of Hawaii at Manoa,2565 McCarthy Mall,Honolulu,HI 96822,USA [3]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Peking Mathematical Journal》2024年第1期247-344,共98页北京数学杂志（英文）

基　　金：R.Liu is partially supported by the National Natural Science Foundation of China under Agreement No.NSFC-11725101 and the Tencent Foundation;N.Truong is partially supported by L.Xiao’s NSF under Grant DMS-1752703;L.Xiao is partially supported by Simons Collaboration under Grant#278433;NSF under Grant DMS-1502147 and DMS-1752703;the Chinese NSF grant NSFC-12071004,Recruitment Program of Global Experts of China,and a grant from the Chinese Ministry of Education;B.Zhao is partially supported by AMS-Simons Travel Grant.

摘　　要：We formulate a local analogue of the ghost conjecture of Bergdall and Pollack,which essentially relies purely on the representation theory of GL_(2)(Q_(p)).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.

关 键 词：Eigencurves Slope of U_(p)operators Overconvergent modular forms Completed cohomology Weight space Gouvêa’s conjecture Gouvêa-Mazur conjecture 

分 类 号：O15[理学—数学]