Attached primes of local cohomology modules under localization and completion

Abstract

In this paper, we study attached primes of H m i ( M ) under localization and m m -adic completion. We prove that the shifted localization principle (1) and the shifted completion principle (2) are both equivalent to the condition that the base ring R is universally catenary and all formal fibers of R are Cohen–Macaulay. The following theorem is the main result of this paper. ... Att R ˆ ( H m i ( M ) ) = ⋃ p ∈ Att R ( H m i ( M ) ) Ass R ˆ ( R ˆ / p R ˆ ) for every finitely generated R-module M and integer i≥0 i ≥ 0 . ... It should be mentioned that the condition (i) in ...