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arXiv · 1605.05398

On growth of systole along congruence coverings of Hilbert modular varieties

Plinio G. P. Murillo
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Abstract

We study how the systole of principal congruence coverings of a Hilbert modular variety grows when the degree of the covering goes to infinity. We prove that given a Hilbert modular variety $M$ of real dimension $2n$, the sequence of principal congruence coverings $M_{I}$ eventually satisfies $$sys\pi_{1}(M_{I})\geq \frac{4}{3\sqrt{n}}\log(vol(M_{I}))-c,$$ where $c$ is a constant independent of $M_{I}$.

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Plinio G. P. Murillo. 2016-05-17. On growth of systole along congruence coverings of Hilbert modular varieties. https://doi.org/10.2140/agt.2017.17.2753

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