Frobenius and multiplicities

DOI10.1016/0021-8693(83)90106-0zbMath0527.13014OpenAlexW1990648816MaRDI QIDQ595713

Sankar P. Dutta

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90106-0

zbMATH Keywords

multiplicityhypersurfacedimensionCohen-Macaulay ringsFrobenius mapHilbert functionGorenstein ringscharacteristic pCM-ringcomplete intersection domainintersection multiplicities of modules

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Homological dimension and commutative rings (13D05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) Complete intersections (14M10) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (32)

A Note on a Conjecture of Watanabe and Yoshida ⋮ Intersection multiplicity of modules in the positive characteristics ⋮ The grade conjecture and asymptotic intersection multiplicity ⋮ Global Frobenius Betti numbers and Frobenius Euler characteristics ⋮ A remark on the Riemann-Roch formula on affine schemes associated with Noetherian local rings ⋮ Lech's conjecture in dimension three ⋮ On the generalized Hilbert-Kunz function and multiplicity ⋮ Globalizing F-invariants ⋮ On the vanishing and the positivity of intersection multiplicities over local rings with small non complete intersection loci ⋮ Uniform bounds in F-finite rings and lower semi-continuity of the F-signature ⋮ Complexes with homology of finite length and Frobenius functors ⋮ Ext and Frobenius ⋮ Generalized Intersection Multiplicities of Modules ⋮ Generalized Intersection Multiplicities of Modules. II ⋮ Lech's inequality, the Stückrad-Vogel conjecture, and uniform behavior of Koszul homology ⋮ Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings ⋮ Intersection multiplicity on blow-ups ⋮ Diagonalizing the Frobenius ⋮ A characterization of Gorenstein rings in characteristic $p\ (>0)$ ⋮ \(F\)-signature exists ⋮ Frobenius functors and invariant factors ⋮ A special case of positivity (II) ⋮ The upper bound of Frobenius related length functions ⋮ Adams operations, localized Chern characters, and the positivity of Dutta multiplicity in characteristic $0$ ⋮ A Special Case of Positivity ⋮ The shape of Hilbert-Kunz functions ⋮ Hilbert-Kunz multiplicity and an inequality between multiplicity and colength ⋮ Hilbert-Kunz functions and Frobenius functors ⋮ Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem. ⋮ Generalized Intersection Multiplicities of Modules ⋮ Modules of finite projective dimension with negative intersection multiplicities ⋮ On modules of finite projective dimension over complete intersections

Cites Work

• Weak linking and multiplicities
• Ringe der Charakteristik p und Frobeniusfunktoren
• Generalized Intersection Multiplicities of Modules
• Characterizations of Regular Local Rings of Characteristic p
• Stable module theory
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