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Calabi-Yau manifolds over finite fields. II. (English) Zbl 1100.14032
Yui, Noriko (ed.) et al., Calabi-Yau varieties and mirror symmetry. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3355-3/hbk). Fields Inst. Commun. 38, 121-157 (2003).
The zeta functions for a one-parameter family of quintic threefolds, defined over a finite field, are calculated. The zeta functions of the mirror manifolds are also calculated by considering the corresponding toric varieties.
For the entire collection see [Zbl 1022.00014].

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
11G25 Varieties over finite and local fields
14G15 Finite ground fields in algebraic geometry