On Jacquet-Langlands isogeny over function fields

2011/03/30 by Mihran Papikian, Papikian, Mihran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1103.5830

29 pages

arxiv created 2011/03/30 · openalex publication_date 2011/03/30 · arxiv updated 2011/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of D-elliptic sheaves. The kernel of the isogeny is a subgroup of the cuspidal divisor group constructed by examining the canonical maps from the cuspidal divisor group into the component groups.

Related

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• Hyperelliptic Jacobians in Isogeny Classes of Abelian Threefolds Over Finite Fields