First coniveau notch of the Dwork family and its mirror
Andre Chatzistamatiou

TL;DR
This paper investigates the relationship between the motives of Dwork family varieties and their mirrors, revealing a coniveau filtration connection that explains certain zeta function congruences over finite fields.
Contribution
It establishes a motivic equivalence up to coniveau 1 between Dwork family members and their mirrors, providing a new perspective on mirror symmetry and zeta function congruences.
Findings
Motives of Dwork family members and their mirrors are equal up to coniveau ≥ 1.
Provides a motivic explanation for Wan's zeta function congruence.
Connects mirror symmetry with coniveau filtration in motives.
Abstract
If is a smooth member of the Dwork family over a perfect field , and is its mirror variety, then the motives of and are equal up to motives that are in coniveau . If is a finite field, this provides a motivic explanation for Wan's congruence between the zeta functions of and .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry
