Intersection Multiplicity of Serre in the Unramified Case

Abstract

We describe here some recent progress pertaining to the Serre Intersection Multiplicity Conjecture. In particular, we show that if A is an unramified regular local ring, then just as in the equicharacteristic case, the intersection multiplicity of two complimentary-dimensional modules is bounded below by the product of their Hilbert-Samuel multiplicities. We also explain, in terms of the blowup of Spec(A) at the closed point, the geometric significance of achieving this lower bound.

arXiv commentThis is a slightly updated version of the original manuscript with changes made to reflect the comments and suggestions of the referee. References have been corrected/added, and the exposition has been modified a bit, most notably in the Introduction