In this paper we study intersection multiplicities of modules as defined by Serre and prove that over regular local rings of dim ≤ 5, given two modules M, N with (FOUMULA PRESENTED). We also study multiplicity in a more general set up. Finally we extend Serre’s result from pairs of modules to pairs of finite free complexes whose homologies are killed by In, Jn, respectively, for some n > 0, with dim R/I + dim R/J < dim R.
ASJC Scopus subject areas
- Applied Mathematics