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Asymptotically good towers and differential equations

Published online by Cambridge University Press:  04 December 2007

Peter Beelen  and
Irene I. Bouw
Peter Beelen
Affiliation:
Universität Duisburg–Essen, Fachbereich Mathematik, Campus Essen, D-45117 Essen, [email protected] Department of Mathematics, Danish Technical University, DK-2800 Kongens Lyngby, Denmark
Irene I. Bouw
Affiliation:
Institut für Experimentelle Mathematik, Ellernstraße 29, D-45326 Essen, [email protected] Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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Abstract

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This paper concerns towers of curves over a finite field with many rational points, following Garcia–Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is the study of algebraic solutions to Fuchsian differential equations modulo p. We apply our results to towers of modular curves, and find new asymptotically good towers.

Keywords

towers of curvesrational points11G20 (primary)14H3514G0514G50 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1405 - 1424
Copyright
Foundation Compositio Mathematica 2005