This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo–Mumford regularity, the Fulton–Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

‘… a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory.’

Source: L’Enseignment Mathématique

‘The book is well organised, very nicely written, and reads very well … a very good overview of local cohomology theory.’

Source: European Mathematical Society

‘I am sure that this will be a standard text and reference book for years to come.’

Liam O’Carroll Source: Bull. London Mathematical Society