First Coniveau Notch of the Dwork Family and Its Mirror

  • Published 2009


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


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