%0 Journal Article %T Frobenius transformation, mirror map and instanton numbers %A Albert Schwarz %A Vadim Vologodsky %J Mathematics %D 2006 %I arXiv %R 10.1016/j.physletb.2008.01.006 %X We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi-Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology . We discuss a $p$-adic interpretation of the conjecture about integrality of Gopakumar-Vafa invariants. %U http://arxiv.org/abs/hep-th/0606151v5