Genus formula for modular curves of D-elliptic sheaves

2009/01/23 by Mihran Papikian, Papikian, Mihran
Mathematics · #11G09 (Primary) #11G18 #11G20 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G09 #msc:11G18 #msc:11G20

paper · pdf · doi:10.48550/arxiv.0901.3641

13 pages, 2 tables

arxiv created 2009/01/23 · openalex publication_date 2009/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a genus formula for modular curves of D-elliptic sheaves. We use this formula to show that the reductions of modular curves of D-elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of D tends to infinity.

Related

• Modular varieties of D-elliptic sheaves and the Weil-Deligne bound
• Genus formulas for families of modular curves
• The class of the d-elliptic locus in genus 2
• Local diophantine properties of modular curves of \calD-elliptic sheaves
• Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on \mathcal M_g