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.

arXiv comment9 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