| Modules Of Finite Length And Finite Projective Dimension (2001) | |||||||||||||||
Abstract | |||||||||||||||
| this paper have their origin in the question of generalizing intersection multiplicities to nonregular commutative rings. If A is a regular local ring of dimension d, and if M and N are two A-modules such that MOmega A N has finite length, then Serre defined the intersection multiplicity of M and N to be (M;N) = d X i=0 (Gamma1) i length (Tor A i (M; N)): Among the properties of this intersection multiplicity is the vanishing theorem, which states that if dim (M)+dim (N) ! d, then (M;N) = 0. (This theorem was proven by Serre in the equicharacteristic case and later proven in general by Gillet and Soul'e [4],[5] and Roberts [12]) | |||||||||||||||
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