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arXiv · 1210.1120

On arithmetic of the superspecial locus

Chia-Fu Yu
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Abstract

We develop a method for describing the Galois action on the superspecial locus of the Siegel moduli space in characteristic $p$. Using this description, we give a modern treatment for the results of Ibukiyama and Katsura [Compos. Math., 1994] concerning the $\mathbb{F}_p$-rational points and the trace of a Hecke operator of Atkin-Lehner type. This also leads to analogues with level-$N$ structure. The trace of the Hecke operator can be reduced into one term (instead of finitely many terms a priori) by the simple trace formula when $N$ is large.

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Chia-Fu Yu. 2012-10-03. On arithmetic of the superspecial locus. https://arxiv.org/abs/1210.1120

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