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Local Cohomology: An Algebraic Introduction with Geometric Applications
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 inExpand
Bass numbers of local cohomology modules
Let A be a regular local ring of positive characteristic. This paper is concerned with the local cohomology modules of A itself, but with respect to an arbitrary ideal of A. The results include thatExpand
Steps in Commutative Algebra
This is an introductory account of commutative algebra. The author's intention is to provide a foundation from which the reader can progress to more advanced works in commutative algebra or algebraicExpand
Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
This paper is concerned with the tight closure of an ideal [a] in a commutative Noetherian local ring R of prime characteristic P. Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N.Expand
Uniform behaviour of the Frobenius closures of ideals generated by regular sequences
This paper is concerned with ideals in a commutative Noetherian ring R of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of R generated by regularExpand
A Method for the Study of Artinian Modules, With an Application to Asymptotic Behavior
If N is a Noetherian module over the commutative ring R (throughout the paper, R will denote a commutative ring with identity), then the study of N in many contexts can be reduced to the study of aExpand
Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings
Abstract This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal a of R, there is a power Q of p, depending on aExpand