Stable reduction of $X_0(p^4)$

Details Stable reduction of $X_0(p^4)$ Stable reduction of $X_0(p^4)$

2011-09-20

arxiv.org/abs/1109.4378v1

Mathematics

Number Theory

41 pages

Scientific paper

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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