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Mirror Congruence for Rational Points on Calabi-Yau Varieties

Lei Fu·Daqing Wan
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Abstract

Wan conjectures that if $X$ and $Y$ form a strong mirror pair of Calabi-Yau varieties over a finite field $F_q$ with $q$ elements, then X and Y have the same number of $F_{q^k}$-rational points modulo $q^k$. We prove this conjecture under the condition that $Y$ can be obtained from $X$ through quotient construction.

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Lei Fu, Daqing Wan. 2005-03-30. Mirror Congruence for Rational Points on Calabi-Yau Varieties. https://arxiv.org/abs/math/0503703

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