2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183154We study integrality of instanton numbers (genus zero Gopakumar - Vafa invariants) for quintic and other Calabi-Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we show that our methods can be used to prove integrality in general case. We give an expression of instanton numbers in terms of Frobenius map on $p$-adic cohomology ; the proof of integrality is based on this expression.10 pages, minor changesHigh Energy Physics - TheoryAlgebraic GeometryNumber Theorytext