In the first part of the talk we will discuss the main statement of local class field theory and discuss the statement of Local Langlands correspondence for $GL_2(K)$, where $K$ is a non-archimedean local field. In the process, we will also introduce all the objects in the statement of correspondence. We will then discuss a brief sketch of the proof of the main statement of local class field theory.

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Last updated: 19 Jul 2024