The Mayer–Vietoris sequence
Any reader with a basic grounding in algebraic topology will recall the important rôle that the Mayer–Vietoris sequence can play in that subject. There is an analogue of the Mayer–Vietoris sequence in local cohomology theory, and it can play a foundational rôle in this subject. It is our intention in this chapter to present the basic theory of the Mayer–Vietoris sequence in local cohomology, and to prepare for several uses of the idea during the subsequent development.
The Mayer–Vietoris sequence involves two ideals, and so throughout this chapter, will denote a second ideal of R (in addition to ). Let M be an