Seminar
MOD p LANGLANDS PROGRAM FOR GLn(Qp)
작성자Author
관리자
작성일Date
20171109 14:26
조회Views
58
분야Field  수학과 전임교원 임용후보자공개 세미나  

날짜Date  20171106  시간Time  5:00 ~ 6:30 
장소Place  Math. Bldg. 404  초청자Host  수학과 
연사Speaker  박 철  소속Affiliation  KIAS/Research Fellow 
TOPIC  MOD p LANGLANDS PROGRAM FOR GLn(Qp)  
소개 및 안내사항Content  Title : MOD p LANGLANDS PROGRAM FOR GLn(Qp) Abstract : Let K be a finite extension of Qp. It is believed that one can attach a smooth Fprepresentation of GLn(K) to a continuous Galois representation Gal(Qp/K) → GLn(Fp) in a natural way, that is called mod p Langlands program for GLn(K). This is known only for GL2(Qp): one of the main difficulties is that there is no classification of such smooth representations of GLn(K) unless K = Qp and n = 2. However, for a given continuous Galois representation ρ0 : Gal(Qp/Qp) → GLn(Fp), one can define a smooth Fprepresentation Π0 of GLn(Qp) by a space of mod p automorphic forms on a compact unitary group, which is believed to be a candidate on the automorphic side corresponding to ρ0 for the mod p Langlands program in the spirit of Emerton. The structure of Π0 is very mysterious as a representation of GLn(Qp), but it is conjectured that Π0 determines ρ0, which is called mod p localglobal compatibility. The weight part of Serre’s conjecture predicts the Serre weights of ρ0, which are defined as the dual of the irreducible Fpsubrepresentations of Π0GLn (Zp ). It is also believed that the set of Serre weights of ρ0 determines ρ0, if ρ0 is semisimple. But this is no longer the case if ρ0 is not semisimple, so that addressing the conjecture, mod p localglobal compatibility, is deeper than the weight part of Serre’s conjecture. In this talk, we introduce these conjectures in more detail and discuss some recent results of the speaker on the weight part of Serre’s conjectures as well as on the mod p localglobal compatibility. We also discuss the Breuil–M´ezard conjecture and its connection to the mod p Langlands program. 
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