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Geometrization of the local Langlands correspondence, motivically

2025/01/14 by Peter Scholze, Scholze, Peter
Mathematics · Physics and Astronomy · #11F77 #11F85 #11S37 #14D24 #14F20 #14F42 #14G22 #14G45 #22E57 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2501.07944

openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the formalism of rigid-analytic motives of Ayoub--Gallauer--Vezzani, we extend our previous work with Fargues from ℓ-adic sheaves to motivic sheaves. In particular, we prove independence of ℓ of the L-parameters constructed there.

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