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arXiv · 1705.01526

Simple connexit\'e des fibres d'une application d'Abel-Jacobi et corps de classe local

Laurent Fargues
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Abstract

We give a geometric Langlands type proof of the geometrization conjecture of the local Langlands correspondence introduced by the author for GL_1. For this we study an Abel-Jacobi morphism. We prove that this morphism is a pro-\'etale locally trivial fibration in simply connected diamonds in high degree. Those diamonds are absolute punctured Banach-Colmez spaces that we study in details.

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Laurent Fargues. 2017-05-03. Simple connexit\'e des fibres d'une application d'Abel-Jacobi et corps de classe local. https://arxiv.org/abs/1705.01526

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