The vanishing of intersection multiplicities of perfect complexes

DOI10.1090/S0273-0979-1985-15394-7zbMath0585.13004OpenAlexW2052681271WikidataQ56286863 ScholiaQ56286863MaRDI QIDQ3710615

Paul C. Roberts

Publication date: 1985

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1985-15394-7

zbMATH Keywords

complete intersectionsintersection multiplicityKrull dimensionsisolated singularitiesregular local ringsperfect complexesNoetherian local ring

Mathematics Subject Classification ID

Related Items (44)

Numerical equivalence defined on Chow groups of Noetherian local rings ⋮ Tensor products of modules and the rigidity of Tor ⋮ Positivity of intersection multiplicity over a two-dimensional base ⋮ A local ring such that the map between Grothendieck groups with rational coefficients induced by completion is not injective ⋮ Openness of the F-rational locus and smooth base change ⋮ Intersection theory using Adams operations ⋮ An intersection formula for CM cycles on Lubin-Tate spaces ⋮ Intersection multiplicity of modules in the positive characteristics ⋮ Quasilength, latent regular sequences, and content of local cohomology ⋮ A new proof of the new intersection theorem ⋮ The grade conjecture and asymptotic intersection multiplicity ⋮ A remark on the Riemann-Roch formula on affine schemes associated with Noetherian local rings ⋮ Local Chern classes, multiplicities, and perfect complexes ⋮ On the vanishing and the positivity of intersection multiplicities over local rings with small non complete intersection loci ⋮ An algebraist commuting in Berkeley ⋮ Serre's vanishing conjecture for Ext-groups. ⋮ Vanishing of Tor, and why we care about it ⋮ Entropy in the category of perfect complexes with cohomology of finite length ⋮ Intersection multiplicity on blow-ups ⋮ Cyclic Adams operations ⋮ Diagonalizing the Frobenius ⋮ An intersection multiplicity in terms of $\textrm {Ext}$-modules ⋮ Test modules to calculate Dutta multiplicities ⋮ A dimension inequality for Cohen-Macaulay rings ⋮ Intersection multiplicity of Serre on regular schemes ⋮ Tilting, cotilting, and spectra of commutative noetherian rings ⋮ Intersection multiplicity of Serre in the unramified case ⋮ A special case of positivity (II) ⋮ Multiplicities and a dimension inequality for unmixed modules ⋮ A theorem on smoothness- Bass-Quillen, Chow groups and intersection multiplicity of Serre ⋮ Lengths of tors determined by killing powers of ideals in a local ring. ⋮ The relative form of Gersten's conjecture over a discrete valuation ring: The smooth case ⋮ Complexity and Tor on a complete intersection ⋮ A Special Case of Positivity ⋮ The shape of Hilbert-Kunz functions ⋮ \(p\)-adic limits of renormalized logarithmic Euler characteristics ⋮ Adams Operations in Commutative Algebra ⋮ Intersection multiplicity over noncommutative algebras ⋮ Constructing modules of finite projective dimension with prescribed intersection multiplicities ⋮ On maps of Grothendieck groups induced by completion. ⋮ Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem. ⋮ A counterexample to the rigidity conjecture for rings ⋮ Tight closure and elements of small order in integral extensions ⋮ On the limit of Frobenius in the Grothendieck group

Cites Work

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• Modules of finite projective dimension with negative intersection multiplicities
• Riemann-Roch for singular varieties
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.

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