Parabolic Simple -invariants and Local-global Compatibility
Time: 2022-11-11
Published By: He Liu
Speaker(s): Yiqin He (PKU)
Time: 11:00-12:00 November 14, 2022
Venue: Room 77201, Jingchunyuan 78, BICMR
Let be a finite extension of and be a potentially semistable noncrystalline -adic representation of such that the associated -semisimple Weil-Deligne representation is absolutely indecomposable. Via a study of Breuil's parabolic simple -invariants, we attach to a locally -analytic representation of , which carries the exact information of the Fontaine-Mazur parabolic simple -invariants of . When comes from a patched automorphic representation of (for a unitary group over a totally real field which is compact at infinite places and at -adic places), we prove under mild hypothesis that is a subrepresentation of the associated Hecke-isotypic subspace of the Banach spaces of (patched) -adic automophic forms on .