|Representation theory of Galois and of GL_2|
|Time：||Tue/Thu 15:10-17:00, 2014-07-03 ~ 2014-07-17|
|Instructor：||Yongquan Hu [Universite de Rennes 1, France]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building|
In this course, we will discuss the modulo p and p-adiclocal Langlands correspondence for GL_2(Q_p), which is established in recent years by Breuil,Colmez, Kisin, Paskunas, etc.
We will firstly talk about modulo p representation theory of GL_2 of a local field F of residual characteristic p, with an emphasis on the caseF=Q_p. We then discuss the construction of a functor of Colmez relating representations of GL_2(Q_p) and representations of the absolute Galois group of Q_p, which plays a crucial role in the theory. Finally, we will pass to their deformation theory and explain the proof of the theoremthat Colmez’sfunctor realizes the p-adic local Langlands correspondence.
Background on representation theory, abstract algebra and algebraic number theory, particularly knowledge on local fields.
1. C. Breuil, Representations of Galois and of GL_2 in characteristic p, lecture notes, 2007.
2. P. Colmez, Representations de GL_2(Q_p) et (phi,Gamma)-modules, Asterisque 330.
3. V. Paskunas, The image of Colmez Montreal functor, Publ. IHES (2013).