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Stable Model of X0(125)

Published online by Cambridge University Press:  01 February 2010

Ken McMurdy
Ken McMurdy
Affiliation:
Dept. of Mathematics, University of Rochester, Rochester, NY 14627, USA, [email protected], http://www.math.rochester.edu/people/facuity/kmcmurdy/

Abstract

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In this paper, the components in the stable model of X0(125) over C5 are determined by constructing (in the language of R. Coleman's ‘Stable maps of curves’, to appear in the Kato Volume of Doc. Math.) an explicit semi-stable covering. Empirical data is then offered regarding the placement of certain CM j-invariants in the supersingular disk of X(1) over C5, which suggests a moduli-theoretic interpretation for the components of the stable model. The paper then concludes with a conjecture regarding the stable model of X0(p3) for p > 3, which is as yet unknown.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 21 - 36
Copyright
Copyright © London Mathematical Society 2004

References

1. Bosch, S., Güntzer, U. and Remmert, R, Non-Archimedean analysis, Grund. Math.Wiss., 261 (Springer, 1984)Google Scholar
2. Buzzard, K., ‘Analytic continuation of overconvergent eigenforms’, J. Amer. Math. Soc. 16, (2003), 29–55.CrossRefGoogle Scholar
3. Coleman, R., ‘On the components of X 0(pn), J. Number Theory, to appear; preprint available at http://www.math.berkeley.edu/~coleman.Google Scholar
4. Coleman, R., ‘Stable maps of curves’, Doc. Math., extra volume:‘Kazuya Kato's Fiftieth Birthday’, (2003), 217–225 available at, http://www.math.uiuc.edu/documents/vol-kato-eng.html.Google Scholar
5. Deline, P., and Rapoport, M., Schemas de modules de courbes elliptiques Lecture Notes in Math. 349 (Springer, New York, 1973), 143–316.Google Scholar
6. Edixhoven, B., ‘Minimal resolution and stable reduction of X 0(N)’, Ann. Inst. Fourier (Grenoble) 40, (1990), 31–67.CrossRefGoogle Scholar
7. Katz, N. and Mazur, B., Arithmetic moduli of elliptic curves, Ann. of Math. Stud. 108, (Princeton university press), (1985).CrossRefGoogle Scholar
8. Lang, S., Elliptic functions, Grad.Texts in Math. 112, (Springer, 1987).Google Scholar
9. McMurdy, K., ‘Explicit parameterizations of ordinary and supersingular regions of X 0(pn)’, Proc., Modular Curves and Abelian Varieties, Barcelona, (2002), to appear.Google Scholar
10. Pizer, A., ‘An algorithm for computing modular forms on Γ0 (N)’, J. Algebra 64, (1980)340–390.CrossRefGoogle Scholar
11. Robert, A., A course in p-adic analysis, Grad. Texts in Math. 198, (Springer, 2000).CrossRefGoogle Scholar