The generically ordinary conjecture for maximally generic Calabi–Yau mirror pairs

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Let d≤3d\leq 3, and let XX and YY be a maximally generic mirror pair of dd-dimensional smooth projective Calabi–Yau schemes over the Witt ring W(Fq)W(\mathbb{F}_q). A reduction is generically ordinary when its generic member is ordinary, meaning that its pp-adic Newton polygon coincides with its Hodge polygon. Generically ordinary conjecture. Both reductions X⊗FqX\otimes\mathbb{F}_q and Y⊗FqY\otimes\mathbb{F}_q are generically ordinary. The conjecture is stated as a slightly stronger assertion implying the slope mirror conjecture in dimensions at most three. The source does not report a proof in this generality.

References

Primary source

Daqing Wan, “Mirror Symmetry For Zeta Functions”, arXiv:math/0411464 (2004).

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