Mathematical Research Letters
Volume 16, Issue 4, July 2009 pp. 563-575.
First coniveau notch of the Dwork family and its mirrorAuthors: Andre Chatzistamatiou
Author institution: Universität Duisburg-Essen
Summary: If $X_{\lambda}$ is a smooth member of the Dwork family over a perfect field $k$, and $Y_{\lambda}$ is its mirror variety, then the motives of $X_{\lambda}$ and $Y_{\lambda}$ are equal up to effective motives that are in coniveau $\geq 1$. If $k$ is a finite field, this provides a motivic explanation for Wan's congruence between the zeta functions of $X_{\lambda}$ and $Y_{\lambda}$.
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