Some fundamental lemmas on projective schemes

Abstract

In this paper we shall prove some fundamental results on invertible sheaves o n projective schemes. All of them are almost trivial when we are working in the worl d of nonnilpotent geometry, but phenomena changes completely when we ar e dealing with general schemes. These topics were brought to our attention during the period of investigation on criterion of ample sheaves on projective schemes(2). We shall borrow notations and terminologies from Grothendieck's book, Elements de geometrie algeibrique, which will be cited as [G].