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March 7, 2026Open Access

Geometrization of the local Langlands correspondence, motivically

Key Points

The aim is to extend the geometrization of the local Langlands correspondence to include motivic sheaves.
Utilized the formalism of rigid-analytic motives.
Built upon previous research focused on ℓ-adic sheaves.
Analyzed the independence of ℓ for the L-parameters.
Proved the independence of ℓ for the constructed L-parameters.
Demonstrated the applicability of motivic sheaves in this context.

Abstract

Abstract Based on the formalism of rigid-analytic motives of J. Ayoub, M. Gallauer and A. Vezzani, The six-functor formalism for rigid analytic motives, Forum Math. Sigma 10 (2022), Paper no. e61, we extend our previous work L. Fargues and P. Scholze, Geometrization of the local Langlands correspondence, preprint (2021), https://arxiv.org/abs/2102.134592021 ; to appear in Astérisque from ℓ-adic sheaves to motivic sheaves. In particular, we prove independence of ℓ of the 𝐿-parameters constructed there.

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Peter Scholze (Thu,) studied this question.

synapsesocial.com/papers/69abc1645af8044f7a4ea029 https://doi.org/https://doi.org/10.1515/crelle-2026-0011

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