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We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, ingenus zero and after an analytic continuation, the quantum singularity theory(FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas ofWitten. Moreover, on both sides, we highlight two remarkable integral localsystems arising from the common formalism of Gamma-integral structures appliedto the derived category of the hypersurface {W=0} and to the category of gradedmatrix factorizations of W. In this setup, we prove that the analyticcontinuation matches Orlov equivalence between the two above categories.

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence