dc.citation.conferencePlace |
KO |
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dc.citation.conferencePlace |
Postech |
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dc.citation.title |
Annual Number Theory Workshop (Number Theory Festival) |
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dc.contributor.author |
Park, Chol |
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dc.date.accessioned |
2024-01-31T23:08:09Z |
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dc.date.available |
2024-01-31T23:08:09Z |
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dc.date.created |
2021-01-04 |
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dc.date.issued |
2020-02-01 |
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dc.description.abstract |
Let K be a finite extension of Qp. It is believed that one can attach a smooth Fp-representation of GLn(K) (or a packet of such representations) to a continuous Galois representation of Gal(K/Qp) with coefficients in 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 R of Gal(K/Qp) with coefficients in GLn(Fp), one can define a smooth Fp-representation P of GLn(K) 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 R for mod p Langlands correspondence in the spirit of Emerton. The structure of P is very mysterious as a representation of GLn(K), but it is conjectured that P determines R, which is called mod-p local-global compatibility. In this talk, we discuss a way to prove this conjecture in the case that R is Fontaine--Laffaille. More precisely, we prove that the tamely ramified part of R is determined by the Serre weights attached to R, and the wildly ramied part of R is obtained in terms of refined Hecke actions on P. This is based on a joint work with Daniel Le, Bao Le Hung, Stefano Morra, and Zicheng Qian. |
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dc.identifier.bibliographicCitation |
Annual Number Theory Workshop (Number Theory Festival) |
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dc.identifier.uri |
https://scholarworks.unist.ac.kr/handle/201301/78622 |
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dc.language |
한국어 |
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dc.publisher |
Postech |
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dc.title |
Fontaine--Laffaille modules and their mod-p local-global compatibility |
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dc.type |
Conference Paper |
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dc.date.conferenceDate |
2020-01-31 |
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