Asymptotically good towers and differential equations

Mathematics – Number Theory

Scientific paper

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Scientific paper

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.

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