English

Geometrization of the local Langlands correspondence, motivically

Algebraic Geometry 2026-01-23 v2 Number Theory Representation Theory

Abstract

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

Keywords

Cite

@article{arxiv.2501.07944,
  title  = {Geometrization of the local Langlands correspondence, motivically},
  author = {Peter Scholze},
  journal= {arXiv preprint arXiv:2501.07944},
  year   = {2026}
}

Comments

27 pages. final version, to appear in Crelle