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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Higher Weierstrass points on $X_{0}(p)$
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by Scott Ahlgren and Matthew Papanikolas
Trans. Amer. Math. Soc. 355 (2003), 1521-1535
DOI: https://doi.org/10.1090/S0002-9947-02-03204-X
Published electronically: November 20, 2002
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Abstract:

We study the arithmetic properties of higher Weierstrass points on modular curves $X_{0}(p)$ for primes $p$. In particular, for $r\in \{2, 3, 4, 5\}$, we obtain a relationship between the reductions modulo $p$ of the collection of $r$-Weierstrass points on $X_{0}(p)$ and the supersingular locus in characteristic $p$.
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Bibliographic Information
  • Scott Ahlgren
  • Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
  • Email: ahlgren@math.uiuc.edu
  • Matthew Papanikolas
  • Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
  • Email: map@math.brown.edu
  • Received by editor(s): July 31, 2002
  • Received by editor(s) in revised form: September 19, 2002
  • Published electronically: November 20, 2002
  • Additional Notes: The first author thanks the National Science Foundation for its support through grant DMS 01-34577
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1521-1535
  • MSC (2000): Primary 11G18; Secondary 11F33, 14H55
  • DOI: https://doi.org/10.1090/S0002-9947-02-03204-X
  • MathSciNet review: 1946403