Frobenius map on local Calabi-Yau manifolds

We prove results that, for a certain class of noncompact Calabi-Yau threefolds, relate the Frobenius action on their p-adic cohomology to the Frobenius action on the p-adic cohomology of the corresponding curves. In the Appendix, we describe our interpretation of the Griffiths-Dwork method.