Asymptotically good towers and differential equations

Peter Beelen; Irene Bouw

doi:10.1112/S0010437X05001624

Asymptotically good towers and differential equations

Peter Beelen
, Irene Bouw

University of Duisburg-Essen

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

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.
Keyword: rational points,towers of curves

Original language	English
Journal	Compositio Mathematica
Volume	141
Issue number	6
Pages (from-to)	1405-1424
ISSN	0010-437X
DOIs	https://doi.org/10.1112/S0010437X05001624
Publication status	Published - 2005
Externally published	Yes

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abstract = "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. Keyword: rational points,towers of curves",

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AB - 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. Keyword: rational points,towers of curves

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DO - 10.1112/S0010437X05001624

M3 - Journal article

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VL - 141

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JO - Compositio Mathematica

JF - Compositio Mathematica

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Asymptotically good towers and differential equations

Abstract

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