Asymptotically good towers and differential equations
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification. Primary 11G20. Secondary: 14H35, 14G05, 14G50.
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