First coniveau notch of the Dwork family and its mirror

Andre Chatzistamatiou
2009 Mathematical Research Letters  
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 effective motives that are in coniveau ≥ 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 .
doi:10.4310/mrl.2009.v16.n4.a2 fatcat:os6kbquruzhbtp3m5bwpf5qixa