# Seminar

# MOD p LANGLANDS PROGRAM FOR GLn(Qp)

작성자Author

관리자

작성일Date

2017-11-09 14:26

조회Views

486

분야Field | 수학과 전임교원 임용후보자공개 세미나 | ||
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날짜Date | 2017-11-06 | 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 Fp-representation 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 Fp-representation 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 local-global compatibility. The weight part of Serre’s conjecture predicts the Serre weights of ρ0, which are defined as the dual of the irreducible Fp-subrepresentations of Π0|GLn (Zp ). It is also believed that the set of Serre weights of ρ0 determines ρ0, if ρ0 is semi-simple. But this is no longer the case if ρ0 is not semi-simple, so that addressing the conjecture, mod p local-global 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 local-global compatibility. We also discuss the Breuil–M´ezard conjecture and its connection to the mod p Langlands program. |

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