Stable reduction of $X_0(p^3)$

Ken McMurdy; Robert Coleman

doi:10.2140/ant.2010.4.357

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Home > Journals > Algebra Number Theory > Volume 4 > Issue 4 > Article

2010 Stable reduction of $X_0(p^3)$

Ken McMurdy, Robert Coleman

Algebra Number Theory 4(4): 357-431 (2010). DOI: 10.2140/ant.2010.4.357

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Abstract

We determine the stable models of the modular curves $X_{0} (p^{3})$ for primes $p \geq 13$ . An essential ingredient is the close relationship between the deformation theories of elliptic curves and formal groups, which was established in the Woods Hole notes of 1964. This enables us to apply results of Hopkins and Gross in our analysis of the supersingular locus.