Orateur
Description
We consider a semi-stable three dimensional p-adic representation ρ of the absolute Galois group of Qp and assume that ρ has rank two monodromy and is non-critical. It is known that ρ depends on three L invariants up to isomorphism. We construct an explicit family of locally analytic representations of GL3(Qp) depending on three invariants and show that there exists a unique representation (conjecturally depends only on ρ) in this family that embeds into a suitable given Hecke eigenspace associated with a global Galois representation whose restriction at p is ρ. We will briefly introduce the construction which involves p-adic dilogarithm and then explain the relation between these representations and previous results by Breuil, Ding and Schraen.
