First coniveau notch of the Dwork family and its mirror
Abstract
Description
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 $Y_λ$.
13 pages, new theorem on the number of rational points of a quotient singularity and a resolution
13 pages, new theorem on the number of rational points of a quotient singularity and a resolution