Local diophantine properties of modular curves of \calD-elliptic sheaves

2010/06/16 by Mihran Papikian, Papikian, Mihran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1006.3237

24 pages

arxiv created 2010/06/16 · openalex publication_date 2010/06/16 · arxiv updated 2010/06/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We study the existence of rational points on modular curves of \calD-elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some applications which include finding presentations for arithmetic groups arising from quaternion algebras, finding the equations of modular curves of \calD-elliptic sheaves, and constructing curves violating the Hasse principle.

Citations

• d-gonality of modular curves and bounding torsions

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