Drinfeld-Stuhler modules and the Hasse principle

2019/08/23 by Keisuke Arai, Arai, Keisuke, Satoshi Kondo +3
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number field #Combinatorics #Computer science #FOS: Mathematics #Hasse principle #Homotopy and Cohomology in Algebraic Topology #Isogeny #Mathematics #Modular design #Multiplication (music) #Number Theory (math.NT) #Pure mathematics #math.NT

paper · pdf · doi:10.48550/arxiv.1908.08678

30 pages

arxiv created 2019/08/23 · openalex publication_date 2019/08/23 · arxiv updated 2019/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a theory of canonical isogeny characters of Drinfeld-Stuhler modules similar to the theory of canonical isogeny characters of abelian surfaces with quaternionic multiplication. We then apply this theory to give explicit criteria for the non-existence of rational points on Drinfeld-Stuhler modular varieties over the finite extensions of \mathbbF_q(T). This allows us to produce explicit examples of Drinfeld-Stuhler curves violating the Hasse principle.

Citations

• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
• D -elliptic sheaves and the langlands correspondence

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