Stable reduction of $X_0(p^4)$

Takahiro Tsushima

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arXiv · 1109.4378

Stable reduction of $X_0(p^4)$

Takahiro Tsushima

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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 ${\rm SL}_2(\mathbb{F}_p).$ We also compute the intersection multiplicity datum in the stable reduction of $X_0(p^4)$.

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Takahiro Tsushima. 2011-09-20. Stable reduction of $X_0(p^4)$. https://arxiv.org/abs/1109.4378

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