2018/07/28 by Ding, Yiwen
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1807.10862
Let L be a finite extension of ℚp, and ρL be an n-dimensional semi-stable non crystalline p-adic representation of GalL with full monodromy rank. Via a study of Breuil's (simple) L-invariants, we attach to ρL a locally ℚp-analytic representation Π(ρL) of GLn(L), which carries the exact information of the Fontaine-Mazur simple L-invariants of ρL. When ρL comes from an automorphic representation of G(\mathbbAF+) (for a unitary group G over a totally real filed F+ which is compact at infinite places and GLn at p-adic places), we prove under mild hypothesis that Π(ρL) is a subrerpresentation of the associated Hecke-isotypic subspaces of the Banach spaces of p-adic automorphic forms on G(\mathbbAF+). In other words, we prove the equality of Breuil's simple L-invariants and Fontaine-Mazur simple L-invariants.