Abstract
This expository paper is based on my lecture at the Borel memory conference. Our main purpose was to explore possible mirror relations between the arithmetic of a Calabi-Yau hypersurface and the arithmetic of its mirror. Through the study of some concrete examples, we discover that there are at least two types of mirror relations between the zeta function of a Calabi-Yau variety and the zeta function of its mirror. The aim of this note is to explain these relations.
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