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arXiv · 2312.01949

Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors

Sheel Ganatra·Andrew Hanlon·Jeff Hicks·Daniel Pomerleano·Nick Sheridan
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Abstract

We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirror symmetry. We also prove homological mirror symmetry for Greene--Plesser mirror pairs in all characteristics such that the B-side family has good reduction, generalizing work of the fifth author and Smith over the complex numbers. A key technical ingredient is a new versality argument which allows us to work throughout over a Novikov-type ring with integer coefficients.

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Sheel Ganatra, Andrew Hanlon, Jeff Hicks, Daniel Pomerleano, Nick Sheridan. 2023-12-04. Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors. https://arxiv.org/abs/2312.01949

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