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- Serre's_multiplicity_conjectures abstract "In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil's initial definition of intersection numbers, around 1949, there had been a question of how to provide a more flexible and computable theory.Let R be a (Noetherian, commutative) regular local ring and P and Q be prime ideals of R. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra. Serre defined the intersection multiplicity of R/P and R/Q by means of the Tor functors of homological algebra, asThis requires the concept of the length of a module, denoted here by lR, and the assumption thatIf this idea were to work, however, certain classical relationships would presumably have to continue to hold. Serre singled out four important properties. These then became conjectures, challenging in the general case. (There are more general statements of these conjectures where R/P and R/Q are replaced by finitely generated modules: see Serre's Local Algebra for more details.)".
- Serre's_multiplicity_conjectures wikiPageID "472700".
- Serre's_multiplicity_conjectures wikiPageRevisionID "501190609".
- Serre's_multiplicity_conjectures hasPhotoCollection Serre's_multiplicity_conjectures.
- Serre's_multiplicity_conjectures subject Category:Commutative_algebra.
- Serre's_multiplicity_conjectures subject Category:Conjectures.
- Serre's_multiplicity_conjectures subject Category:Intersection_theory.
- Serre's_multiplicity_conjectures type Abstraction100002137.
- Serre's_multiplicity_conjectures type Cognition100023271.
- Serre's_multiplicity_conjectures type Concept105835747.
- Serre's_multiplicity_conjectures type Conjectures.
- Serre's_multiplicity_conjectures type Content105809192.
- Serre's_multiplicity_conjectures type Hypothesis105888929.
- Serre's_multiplicity_conjectures type Idea105833840.
- Serre's_multiplicity_conjectures type PsychologicalFeature100023100.
- Serre's_multiplicity_conjectures type Speculation105891783.
- Serre's_multiplicity_conjectures comment "In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil's initial definition of intersection numbers, around 1949, there had been a question of how to provide a more flexible and computable theory.Let R be a (Noetherian, commutative) regular local ring and P and Q be prime ideals of R.".
- Serre's_multiplicity_conjectures label "Serre's multiplicity conjectures".
- Serre's_multiplicity_conjectures sameAs m.02dprb.
- Serre's_multiplicity_conjectures sameAs Q7455403.
- Serre's_multiplicity_conjectures sameAs Q7455403.
- Serre's_multiplicity_conjectures sameAs Serre's_multiplicity_conjectures.
- Serre's_multiplicity_conjectures wasDerivedFrom Serre's_multiplicity_conjectures?oldid=501190609.
- Serre's_multiplicity_conjectures isPrimaryTopicOf Serre's_multiplicity_conjectures.