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FIELD Math: CMC
DATE January 14 (Mon), 2019
TIME 15:00-17:00
PLACE 8101
SPEAKER Yiwen Ding
HOST Park, Chol
INSTITUTE Peking University
TITLE [Lecture Series on Number Theory] L-invariants and p-adic Langlands program, Lecture I
ABSTRACT

To a semi-stable non-crystalline p-adic Galois representation, one can associate the so-called Fontaine-Mazur L-invariants. Such invariants are however invisible in the classical local Langlands correspondence. A task in p-adic Langlands program is therefore to understand their counterpart in p-adic automorphic representations. In these lectures, we will first review some of Breuil's work on L-invariants in GL2(Qp)-case (which somehow initialized the p-adic Langlands program). Then we discuss some joint work with Breuil on L-invariants in GL3(Qp)-case. We will explain the construction, based on p-adic Langlands correspondence for GL2(Qp), of a locally analytic representation of GL3(Qp) which carries the information of all the L-invariants. We will also show a local-global compatiblity result on L-invariants.

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