Frobenius transformation, mirror map and instanton numbers

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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.
13 pages,new section about Gopakumar-Vafa invariants added, some additions in the last section, some corrections

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