In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite...In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called rigid.Second,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.展开更多
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 ...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.展开更多
The issue of local and global conjugacy is closely related to the multiplicity one property in representation theory and the Langlands program. In this article we give first families of connected instances for SO2N wh...The issue of local and global conjugacy is closely related to the multiplicity one property in representation theory and the Langlands program. In this article we give first families of connected instances for SO2N where the multiplicity one fails in both aspects of representation theory and automorphic forms with certain assumptions on the Langlands functoriality.展开更多
In this paper we study the derivatives of Frobenius and the derivatives of Hodge–Tate weights for families of Galois representations with triangulations.We generalize the Fontaine–Mazur L-invariant and use it to bui...In this paper we study the derivatives of Frobenius and the derivatives of Hodge–Tate weights for families of Galois representations with triangulations.We generalize the Fontaine–Mazur L-invariant and use it to build a formula which is a generalization of the Colmez–Greenberg–Stevens formula.For the purpose of proving this formula we show two auxiliary results called projection vanishing property and"projection vanishing implying L-invariants"property.展开更多
基金Y.L.supported by NSF(Grant No.DMS-1702019)and a Sloan Research FellowshipY.T.supported by NSFC(Grant No.12225112/12231001)+4 种基金CAS Project for Young Scientists in Basic Research(Grant No.YSBR-033)L.X.supported by NSF(Grant No.DMS-1502147/DMS-1752703)NSFC(Grant No.12071004)and the Chinese Ministry of EducationW.Z.supported by NSF(Grant No.DMS-1838118/DMS-1901642)X.Z.supported by NSF(Grant No.DMS-1902239)and a Simons Fellowship。
文摘In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called rigid.Second,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.
基金supported by the C.N.R.S and is a member of the A.N.R.project CLap-CLap ANR-18-CE40-0026supported by the NSFC Grant No.8200905010 and No.8200800065.
文摘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.
基金National Natural Science Foundation of China (Grant No. A010102-11671380)One Hundred Talents Program at Chinese Academy of Sciences, National Basic Research Program of China (Grant No. 2013CB834202)National Science Foundation of USA (Grant No. DMS9729992)。
文摘The issue of local and global conjugacy is closely related to the multiplicity one property in representation theory and the Langlands program. In this article we give first families of connected instances for SO2N where the multiplicity one fails in both aspects of representation theory and automorphic forms with certain assumptions on the Langlands functoriality.
基金the National Natural Science Foundation of China(Grant No.11671137)。
文摘In this paper we study the derivatives of Frobenius and the derivatives of Hodge–Tate weights for families of Galois representations with triangulations.We generalize the Fontaine–Mazur L-invariant and use it to build a formula which is a generalization of the Colmez–Greenberg–Stevens formula.For the purpose of proving this formula we show two auxiliary results called projection vanishing property and"projection vanishing implying L-invariants"property.
