×

Cofiniteness of local cohomology modules for principal ideals. (English) Zbl 0930.13013

In this note we show that, if an ideal \(I\) of a Noetherian ring is principal, up to radical, then the local cohomology modules with support in \(V(I)\) are \(I\)-cofinite.

MSC:

13D45 Local cohomology and commutative rings
14B15 Local cohomology and algebraic geometry
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI