## 代数学コロキウム

開催情報 水曜日　17:00～18:00　数理科学研究科棟(駒場) 056号室 今井 直毅，ケリー シェーン

### 2007年12月05日(水)

16:30-17:30   数理科学研究科棟(駒場) 117号室

Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).