Algebraic spaces

Michael Artin9780300013962, 0300013965

These notes are based on lectures given at Yale University in the spring of 1969. Their object is to show how algebraic functions can be used systematically to develop certain notions of algebraic geometry,which are usually treated by rational functions by using projective methods. The global structure which is natural in this context is that of an algebraic space—a space obtained by gluing together sheets of affine schemes by means of algebraic functions.I tried to assume no previous knowledge of algebraic geometry on thepart of the reader but was unable to be consistent about this. The attempt only prevented me from developing any topic systematically. Thus,at best, the notes can serve as a naive introduction to the subject.