Representations of the Kottwitz gerbes

2022/05/13 by Sergei Iakovenko, Iakovenko, Sergei
Mathematics · #11G09 #11R32 #11R39 #14G25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2205.06510

openalex publication_date 2022/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a local or global field and let G be a linear algebraic group over F. We study Tannakian categories of representations of the Kottwitz gerbes Rep(Kt_F) and the functor G↦ B(F, G) defined by Kottwitz in [28]. In particular, we show that if F is a function field of a curve over \mathbbF_q, then Rep(Kt_F) is equivalent to the category of Drinfeld isoshtukas. In the case of number fields, we establish the existence of various fiber functors on Rep(Kt_ℚ) and its subcategories and show that Scholze's conjecture [41, Conjecture 9.5] follows from the full Tate conjecture over finite fields [47].

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