Canonical elements in local cohomology modules and the direct summand conjecture

DOI10.1016/0021-8693(83)90092-3zbMath0562.13012OpenAlexW2089196151WikidataQ123142791 ScholiaQ123142791MaRDI QIDQ2266742

Publication date: 1983

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2027.42/25107

zbMATH Keywords

formal power series ring local cohomology canonical modules direct summand conjecture syzygy problem Canonical element conjecture intersection conjecture modules of syzygies property CE

Mathematics Subject Classification ID

(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Deformations and infinitesimal methods in commutative ring theory (13D10) Local deformation theory, Artin approximation, etc. (14B12)

Related Items

Buchsbaum and Monomial Conjecture Dimension, Degree \(p\) extensions of an unramified regular local ring of mixed characteristic \(p\), Big Cohen-Macaulay modules, morphisms of perfect complexes, and intersection theorems in local algebra, On the canonical element conjecture. II, Finite super height of a homogeneous ideal in \({\mathbb{Z}}^ n\)-graded extensions, Maximal Cohen-Macaulay Complexes and Their Uses: A Partial Survey, The direct summand conjecture for some bigenerated extensions and an asymptotic version of Koh's conjecture, Intersection multiplicity, canonical element conjecture and the syzygy problem, Almost regular sequences and the monomial conjecture, Splitting results in module-finite extension rings and Koh's conjecture, On the direct summand conjecture and its derived variant, Closure operations that induce big Cohen-Macaulay modules and classification of singularities, On the Gorenstein property of Rees algebras, The direct factor conjecture, Quasilength, latent regular sequences, and content of local cohomology, On the support of local cohomology, Skew-polynomial rings of frobenius type and the theory of tight closure, Tight closure and strong F-regularity, Finite Tor dimension and failure of coherence in absolute integral closures, Lower bounds on projective levels of complexes, Cohen-Macaulay properties of ring homomorphisms, Content of local cohomology, parameter ideals, and robust algebras, On some permanence properties of (derived) splinters, Openness of splinter loci in prime characteristic, Reductions towards a characteristic free proof of the Canonical Element Theorem, Mixed characteristic homological theorems in low degrees., Stiffness of finite free resolutions and the canonical element conjecture., Closure operations that induce big Cohen-Macaulay algebras, On some conditions of regularity, in terms of existence of a good basis of syzygies, A sufficient condition for \(F\)-purity, Ext and Frobenius, The monomial conjecture and order ideals, Koh like theorems for polynomials in mixed characteristic, Direct summand conjecture and descent for flatness, Syzygy theorems via comparison of order ideals on a hypersurface, Little dimension and the improved new intersection theorem, Generalized local cohomology and the canonical element conjecture, Tightly closed ideals, Almost direct summands, Fontaine rings and local cohomology, Finiteness properties and numerical behavior of local cohomology, Free resolutions of parameter ideals for some rings with finite local cohomology, Singularities in mixed characteristic. The perfectoid approach, Homological properties of the perfect and absolute integral closures of noetherian domains, Splitting of local cohomology of syzygies of the residue field, On the Canonical Element Conjecture, Local cohomology of module of differentials of integral extensions, On superheight conditions for the affineness of open subsets., Koszul and local cohomology, and a question of Dutta, Towards a homological generalization of the direct summand theorem, Some restrictions on the maps in minimal resolutions, Normality and Related Properties of Forcing Algebras, A note on the strong direct summand conjecture, Generalized fractions and the monomial conjecture, On the structure of the endomorphism ring of a certain local cohomology module, A note on the syzygy problem, A Note on the Monomial Conjecture, Connections between reduced Bass numbers and Auslander's \(\delta\)-invariant, On the notion of Cohen-Macaulayness for non-Noetherian rings, New homological invariants for modules over local rings. II, Local cohomology of module of differentials of integral extensions. II, Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem., Monomial conjecture and complete intersections, Tight closure and elements of small order in integral extensions, The monomial conjecture and order ideals. II

Cites Work