  For any closed symplectic manifold, we show that the number of 1-periodic
orbits of a nondegenerate Hamiltonian thereon is bounded from below by a
version of total Betti number over Z of the ambient space taking account of the
total Betti number over Q and torsions of all characteristic. The proof is
based on constructing a Hamiltonian Floer theory over the Novikov ring with
integer coefficients, which generalizes our earlier work for constructing
integer-valued Gromov-Witten type invariants. In the course of the
construction, we build a Hamiltonian Floer flow category with compatible smooth
global Kuranishi charts. This generalizes a recent work of
Abouzaid-McLean-Smith, which might be of independent interest.
