We show that crystals with the properties of crystalline cohomology
of ordinary Calabi-Yau threefolds in characteristic p > 0,
exhibit a remarkable similarity with the well known structure on the
cohomology of complex Calabi-Yau threefolds near a boundary point of
the moduli space with maximal unipotent local monodromy. In particular,
there are canonical coordinates and an analogue of the prepotential
of the Yukawa coupling. Moreover in Formulas (2.25) and (2.29) we
show p-adic analogues of the integrality properties for the canonical coordinates
and the prepotential of the Yukawa coupling, which have been
observed in the examples of Mirror Symmetry.
http://www.arxiv.org/abs/math.AG/021206
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