$p$-Ordinary Part of Hyperbolic Cycles on Modular Curves

Hohto Bekki; Ryotaro Sakamoto

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arXiv · 2603.21945

$p$-Ordinary Part of Hyperbolic Cycles on Modular Curves

Hohto Bekki·Ryotaro Sakamoto

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Abstract

In this paper, we study hyperbolic cycles in the first homology group with local coefficients of congruence subgroups of $\mathrm{SL}_2(\mathbb{Z})$. We prove that, for any prime number $p$, the $p$-ordinary part of the first homology group is generated by hyperbolic cycles.

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Hohto Bekki, Ryotaro Sakamoto. 2026-03-23. $p$-Ordinary Part of Hyperbolic Cycles on Modular Curves. https://arxiv.org/abs/2603.21945

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