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Genus formula for modular curves of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-elliptic sheaves

Authors
  • Papikian, Mihran1
  • 1 Pennsylvania State University, Department of Mathematics, University Park, PA, 16802, USA , University Park (United States)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Birkhäuser-Verlag
Publication Date
Mar 27, 2009
Volume
92
Issue
3
Pages
237–250
Identifiers
DOI: 10.1007/s00013-009-3102-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

We prove a genus formula for modular curves of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-elliptic sheaves. We use this formula to show that the reductions of modular curves of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} tends to infinity.

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