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Transactions of the American Mathematical Society

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Higher Weierstrass points on $X_{0}(p)$
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by Scott Ahlgren and Matthew Papanikolas PDF
Trans. Amer. Math. Soc. 355 (2003), 1521-1535 Request permission

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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Additional 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