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arXiv · 0804.2472

First coniveau notch of the Dwork family and its mirror

Andre Chatzistamatiou
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Abstract

If $X_λ$ is a smooth member of the Dwork family over a perfect field $k$, and $Y_λ$ is its mirror variety, then the motives of $X_λ$ and $Y_λ$ are equal up to 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 $X_λ$ and $Y_λ$.

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Andre Chatzistamatiou. 2009-03-05. First coniveau notch of the Dwork family and its mirror. https://arxiv.org/abs/0804.2472

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