Positivity of Intersection Multiplicity Over a Two-Dimensional Base

Abstract

We show that Serre's Intersection Multiplicity Conjecture holds for a formal power series ring A over a complete, two-dimensional regular local ring R. From this, we deduce the corresponding result for the local rings of any scheme X which is a smooth extension of a regular, two-dimensional base Y. We also investigate the connection between intersection multiplicity and transversality in the unramified setting via a local analysis on the blowup.

arXiv commentTo appear in the Journal of Pure and Applied Algebra. Typos from the original draft have been fixed along with some minor changes in exposition to improve clarity