Morse inequalities for covering manifolds

We study the existence of L-2 holomorphic sections of invariant line bundle s over Galois coverings. We show that the von Neumann dimension of the spac e of L-2 holomorphic sections is bounded below under weak curvature conditi ons. We also give criteria for a compact complex space with isolated singul arities and some related strongly pseudoconcave manifolds to be Moishezon. As applications we prove the stability of the previous Moishezon pseudoconc ave manifolds under perturbation of complex structures as well as weak Lefs chetz theorems.