Arnold Conjecture Over Integers

We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number over Z, which takes account of torsions of all characteristics. The proof relies on an abstract perturbation scheme (FOP perturbations) which allows us to produce integral pseudo-cycles from moduli space of J-holomorphic curves, and a geometric regularization scheme for moduli space of Hamiltonian Floer trajectories generalizing the recent work of Abouzaid-McLean-Smith. I will survey these ideas and indicate potential future developments. This is joint work with Guangbo Xu.