On set theoretically and cohomologically complete intersection ideals

Abstract

Let $(R,\fm)$ be a local ring and $\fa$ be an ideal of $R$. The inequalities $$\begin{array}{ll} \ \Ht(\fa) \leq \cd(\fa,R) \leq \ara(\fa) \leq l(\fa) \leq μ(\fa) \end{array}$$ are known. It is an interesting and long-standing problem to find out the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities.

9 pages, to appear in Canad. Math. Bull

References in corpus (2)

• On the arithmetical rank of certain monomial ideals
• On cohomologically complete intersections

Cited by in corpus (5)

• On cohomological invariants of local rings in positive characteristic
• A note on the use of Frobenius map and D-modules in local cohomology
• Lyubeznik Tables of Ideals of Cycle Graphs
• On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers
• On cohomological dimension and depth under linkage