On growth of systole along congruence coverings of Hilbert modular varieties

Pino Murillo, Plinio Guillel (2017). On growth of systole along congruence coverings of Hilbert modular varieties. Algebraic and geometric topology, 17(5), pp. 2753-2762. Geometry & Topology Publications 10.2140/agt.2017.17.2753

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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 Mk of real dimension 2n defined over a number field k, the sequence of principal congruence coverings MI eventually satisfies sys₁(MI)≥4 /3√n log(vol(MI))−c,
where c is a constant independent of MI.

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