2023/12/04 by Ganatra, Sheel, Hanlon, Andrew, Hicks, Jeff +2 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2312.01949
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.