Stable reduction of $X_0(p^4)$

Abstract

R. Coleman and K. McMurdy compute the stable reduction of $X_0(p^3).$ On the basis of their ideas, we compute the stable reduction of $X_0(p^4).$ As a result, in the stable reduction of $X_0(p^4)$, we find irreducible components, defined by $a^p-a=t^{p+1}$. These components are called Deligne-Lusztig curve for ${\mathrm{SL}}_2({\mathbb{F}}_p).$ We also compute the intersection multiplicity datum in the stable reduction of $X_0(p^4)$.

arXiv comment41 pages

Cited by in corpus (1)

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