Where to read about sheaves?

Question

I'm working through Mumford's Red Book, and after introducing the definition of a sheaf, he says "Sheaves are almost standard nowadays, and we will not develop their properties in detail." So I guess I need another source to read about sheafs from. Does anybody know of any expository papers that cover them? I'd prefer to not have to dig deep into a separate textbook if possible.

Answer 1

I understand that you don't want to dig deep into a separate text book of Sheaf Theory. Still my suggestion would Sheaf Theory by B. R. Tennison. It is a 163 page book. But just for the introduction to sheaf you can just read the first two chapters of it, which is some 30 pages. The book is self content. It is very detailed (For example, he defines inductive limit in order to define stalk of a sheaf at a point).

Answer 2

One relatively old but classic reference is Serre's paper "Faisceaux Algébriques Cohérents", often referred to simply as FAC. English translations can be found fairly easily online (see for instance here).

Another reference is the book The Geometry of Schemes by Eisenbud and Harris. They cover sheaves before moving on to schemes.

Answer 3

I suggest Mumford and Oda - Algebraic Geometry II (a penultimate draft), the appendix at the first chapter; so one finds again the style of Mumford.