2022/07/26 by Alexander Bertoloni Meli, Meli, Alexander Bertoloni, Linus Hamann +3
Mathematics · #11S37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2207.13193
openalex publication_date 2022/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study unramified unitary and unitary similitude groups in an odd number of variables. Using work of the first and third named authors on the Kottwitz Conjecture for the similitude groups, we show that the Fargues--Scholze local Langlands correspondence agrees with the semi-simplification of the local Langlands correspondences constructed by Mok for the groups we consider. This compatibility result is then combined with the spectral action constructed by Fargues--Scholze, to verify their categorical form of the local Langlands conjecture for supercuspidal ℓ-parameters. We deduce Fargues' eigensheaf conjecture and prove the strongest form of Kottwitz's conjecture for the groups we consider, even in the case of non minuscule μ.