AN ELEMENTARY PROOF OF THE NON-VANISHING OF CERTAIN LOCAL COHOMOLOGY MODULES

DOI10.1093/qmath/23.2.197zbMath0235.14004OpenAlexW1976380347MaRDI QIDQ5644085

Rodney Y. Sharp, Macdonald, I. G.

Publication date: 1972

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/qmath/23.2.197

Mathematics Subject Classification ID

Local cohomology and commutative rings (13D45) Local cohomology and algebraic geometry (14B15) Relevant commutative algebra (14A05)

Related Items (34)

Surjectivity of some local cohomology map and the second vanishing theorem ⋮ Graded Local Cohomology: Attached and Associated Primes, Asymptotic Behaviors ⋮ Krull dimension and generalized fractions ⋮ Vanishing of the top local cohomology modules over noetherian rings ⋮ Some Rigidity Results for Highest Order Local Cohomology Modules ⋮ Top Local Cohomology Modules ⋮ Some applications of a criterion for Artinianness of a module ⋮ Artinian cofinite top local cohomology modules on derived category ⋮ A Note on the Artinianness and Vanishing of Local Cohomology and Generalized Local Cohomology Modules ⋮ Constructions of artinian modules ⋮ Attached primes of local cohomology modules of complexes ⋮ Unnamed Item ⋮ Some homological invariants of local PI algebras ⋮ Secondary representations for injective modules over commutative Noetherian rings ⋮ On the finiteness of Bass numbers of local cohomology modules ⋮ Local cohomology and the Cousin complex for a commutative Noetherian ring ⋮ Weitere Bemerkungen zu einem Problem der Schnittheorie und über ein Maß\ von A. Seidenberg für die Imperfektheit ⋮ Generalized fractions and Hughes' gradetheoretic analogue of the Cousin complex ⋮ Artinianness of formal local cohomology modules ⋮ ATTACHED PRIMES OF THE TOP GENERALIZED LOCAL COHOMOLOGY MODULES ⋮ Top local cohomology modules with respect to a pair of ideals ⋮ On Grothendieck's local duality theorem ⋮ Generalized fractions and the monomial conjecture ⋮ On the non-vanishing of local cohomology modules ⋮ Cohen–Macaulay Loci of Modules ⋮ Attached primes of local cohomology modules with respect to a pair of ideals ⋮ On the Attached Prime Ideals of Local Cohomology Modules ⋮ On the attached prime ideals of certain Artinian local cohomology modules ⋮ On the attached prime ideals of certain Artinian local cohomology modules ⋮ Local cohomology and modules of generalized fractions ⋮ Filter regular sequences and generalized local cohomology modules ⋮ Lengths of certain generalized fractions ⋮ Some results on top local cohomology and top formal local cohomology modules ⋮ Reduced Bass numbers, Auslanders δ-invariant and certain homological conjectures

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