First steps towards p-adic Langlands functoriality

First steps towards p-adic Langlands functoriality

— By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type ...

4 TOWARDS A p - ADIC LANGLANDS PROGRAMME

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Langlands Functoriality Conjecture

Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which a...

Lecture on Langlands Functoriality Conjecture

First Steps with the Langlands Program∗

This article describes ways in which to get an overview of some of the goals and methods of Langlands program, and it points to treatments of some examples that are worth keeping in mind.