2025/05/25 by Choi, Yong-Gyu, Wansu Kim, Kim, Wansu +2
Mathematics · #14D23 #14G35 #14H60 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2505.18977
openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a maximal order D of a central division algebra over a global function field F, we prove an explicit sufficient condition for moduli stacks of D^×-shtukas to be proper over a finite field in terms of the local invariants of D and bounds. Our proof is a refinement of E.~Lau's result (Duke Math. J. 140 (2007)), which showed the properness of the leg morphism (or characteristic morphism) away from the ramification locus of D. We also establish non-emptiness of Newton and Kottwitz--Rapoport strata for moduli stacks of B^×-shtukas, where B is a maximal order of a central simple algebra over F.