Mirror Congruence for Rational Points on Calabi-Yau Varieties

Details Mirror Congruence for Rational Points on Calabi-Yau Varieties Mirror Congruence for Rational Points on Calabi-Yau Varieties

2005-03-30

arxiv.org/abs/math/0503703v1

Mathematics

Algebraic Geometry

Scientific paper

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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