Best book to learn local cohomology with a global point of view Can anyone suggest me some book that we can use for studying local cohomology, with a global view to many different area of maths, i.e  to Commutative Algebra, Number Theory, Algebraic Geometry....
I have finished reading "Commutative Algebra, Atiyah-Mac Donald",  "Elementary Algebraic Geometry-Hulek", I also have a solid background on homological algebra.
Please help me. Thanks alot.
 A: The book Twenty-Four Hours of Local Cohomology  seems to be exactly what you are looking for.
It is an outgrowth by seven authors of a summer school on the subject held in Utah in 2005.       
As the amusing title says, the book is divided into 24 short chapters, reflecting the 24 talks of the school.
These chapters are extremely easy and chock-full of examples and explicit computations.
The prerequisites are at a very low level and the first few chapters will probably be a just a reminder for you: definition of affine algebraic varieties over a field, sheaves and  Čech cohomology, resolutions, limits, ...
Local cohomology is only introduced in chapter 7, in a  friendly way.  
A bonus of that book is that the chapters are so well constructed that one can learn a lot of independent material from them, even if one isn't  interested in local cohomology!
For example Chapter 19 is a pleasant introduction to Grothendieck's algebraic version of De Rham cohomology; its relation to local cohomology is evoked only at the end of the chapter.
The level is  so elementary that the first section   starts with a proof of Green's theorem of  "advanced" calculus!
A: From my point of view, bearing in mind your previous background, I would suggest the following book:
M. P. Brodmann and R. Y. Sharp. Local Cohomology: An algebraic introduction with geometric applications.
It only requires a very basic knowledge of Commutative Algebra and Homological Algebra.
