Unbranched Riemann Domains over Q-Complete Spaces

Abstract

It is proved that if X is an unbranched Riemann domain and locally r-complete morphism over a q-complete space then X is cohomo- logically q r 1 -complete if q 2 We have shown in 1 that if X is an unbranched Riemann domain and locally q-complete morphism over a Stein space then X is cohomologically q-complete with respect to the struc- ture sheaf In section 4 of this article we prove by means of a counterexample that that there exists for each integer n 3 an open subset Cn which is locally n 1 -complete but is not n 1 -complete The counterexample we give is obtained by making a slight modification of a recent example given by the author 2