%0 Journal Article %T Frobenius map on local Calabi-Yau manifolds %A I. Shapiro %J Mathematics %D 2008 %I arXiv %R 10.1063/1.3075574 %X We prove results that, for a certain class of non-compact 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. %U http://arxiv.org/abs/0810.2195v1