Arnold conjecture over integers

We will discuss the following version of the homological Arnold conjecture: for any closed symplectic manifold, the number of 1-periodic orbits of a 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 key input is a perturbation scheme proposed by Fukaya-Ono and realized by joint work with Xu, which allows us to extract integer-valued invariants from moduli spaces of pseudo-holomorphic curves, except solving the usual regularity problem for these moduli spaces. This is joint work with Guangbo Xu.