Bernstein Eigenvarieties  

作　　者：Christophe Breuil Yiwen Ding 

机构地区：[1]CNRS,Batiment 307,Faculte d’Orsay,Universite Paris-Saclay,91405 Orsay Cedex,France [2]BICMR,Peking University,No.5 Yiheyuan Road Haidian District,Beijing 100871,China

出　　处：《Peking Mathematical Journal》2024年第2期471-642,共172页北京数学杂志（英文）

基　　金：supported by the C.N.R.S and is a member of the A.N.R.project CLap-CLap ANR-18-CE40-0026;supported by the NSFC Grant No.8200905010 and No.8200800065.

摘　　要：We construct parabolic analogues of(global)eigenvarieties,of patched eigenvarieties and of(local)trianguline varieties,that we call,respectively,Bernstein eigenvarieties,patched Bernstein eigenvarieties,and Bernstein paraboline varieties.We study the geometry of these rigid analytic spaces,in particular(generalising results of Breuil-Hellmann-Schraen)we show that their local geometry can be described by certain algebraic schemes related to the generalised Grothendieck-Springer resolution.We deduce several local-global compatibility results,including a classicality result(with no trianguline assumption at p),and new cases towards the locally analytic socle conjecture of Breuil in the non-trianguline case.

关 键 词：Galois representation Automorphic representation Eigenvariety Parabolic group Companion constituent Bernstein center 

分 类 号：O17[理学—数学]