A theorem on smoothness- Bass-Quillen, Chow groups and intersection multiplicity of Serre

DOI10.1090/S0002-9947-99-02372-7zbMath0945.13007OpenAlexW1824356518MaRDI QIDQ4942853

Sankar P. Dutta

Publication date: 15 March 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02372-7

zbMATH Keywords

Chow groupsArtin's approximation theoremSerre's conjecture on intersection multiplicitiessmoothness for regular local rings

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Homological conjectures (intersection theorems) in commutative ring theory (13D22) (Equivariant) Chow groups and rings; motives (14C15) Regular local rings (13H05) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items

Intersection multiplicity of modules in the positive characteristics ⋮ Lech's conjecture in dimension three ⋮ On the relationship between depth and cohomological dimension ⋮ Intersection multiplicity on blow-ups ⋮ ¹-Homotopy of Chevalley Groups ⋮ Intersection multiplicity of Serre in the unramified case ⋮ Chevalley groups of polynomial rings over Dedekind domains ⋮ Decent intersection and Tor-rigidity for modules over local hypersurfaces ⋮ On triviality of the Euler class group of a deleted neighbourhood of a smooth local scheme

Cites Work

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• Efficient generation of ideals in polynomial rings
• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Modules of finite projective dimension with negative intersection multiplicities
• On the Bass-Quillen conjecture concerning projective modules over polynomial rings
• An approach to the characteristic free Dutta multiplicity
• On Chow groups and intersection multiplicity of modules. II
• The relative form of Gersten's conjecture over a discrete valuation ring: The smooth case
• On the vanishing of Tor in regular local rings
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.
• Generalizations of the notion of class group
• Algebraic approximation of structures over complete local rings
• The vanishing of intersection multiplicities of perfect complexes
• A Special Case of Positivity
• Higher algebraic K-theory: I