Asymptotically good towers and differential equations

Peter Beelen, Irene Bouw

Research output: Contribution to journalJournal articleResearchpeer-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 languageEnglish
JournalCompositio Mathematica
Volume141
Issue number6
Pages (from-to)1405-1424
ISSN0010-437X
DOIs
Publication statusPublished - 2005
Externally publishedYes

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