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# Mathematical Research Letters

## Volume 16 (2009)

### Number 4

### First coniveau notch of the Dwork family and its mirror

Pages: 563 – 575

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n4.a2

#### Author

#### Abstract

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 $Y_{\lambda}$.