First coniveau notch of the Dwork family and its mirror

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

2008-04-15

arxiv.org/abs/0804.2472v3

Mathematics

Algebraic Geometry

13 pages, new theorem on the number of rational points of a quotient singularity and a resolution

Scientific paper

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 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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