  We give a simplified derivation of the expression of instanton numbers and of
mirror map in terms of Frobenius map on p-adic cohomology and use this
expression to prove integrality theorems. Modifying this proof we verify that
the Aganagic-Vafa formulas for the number of holomorphic disks can be expressed
in terms of Frobenius map on p-adic relative cohomology; this expression
permits us to prove integrality of this number.
