Noncommutative Projective Spectrum

Abstract

It is not our purpose here to develop a full size noncommutative projective geometry. What follows is a few sketchy fragments of the picture, just to explain the basics and to show that the commutative projective geometry is a special case of some more general, very natural (and very promising) phenomena. We restrict ourselves to the ‘elementary analysis’ (in terminology of EGA); i.e. we do not use cohomology which provide the most appropriate tools and language to study non-affine ‘spaces’. A detailed exposition (including cohomological study and analysis of main motivating examples, like quantized flag varieties) would considerably change the volume and the character of this book. So that it shall appear elsewhere.