A vanishing theorem for quadratic intersection multiplicities

TL;DR

This paper proves a vanishing theorem for quadratic intersection multiplicities within Chow-Witt groups, extending Serre's classical result to a quadratic setting over perfect fields.

Contribution

It establishes a vanishing property for products in Chow-Witt groups when supports do not intersect properly, generalizing Serre's intersection multiplicity theorem.

Findings

Product maps vanish when supports do not intersect properly

Extension of Serre's vanishing theorem to quadratic intersection theory

Provides new tools for intersection theory in algebraic geometry

Abstract

We study intersection theoretic problems in the setting of Chow-Witt groups with coefficients in a fixed Milnor-Witt cycle algebra over a perfect field. We prove that the product maps on such groups satisfy the following property: given two points in a regular local scheme with supports which do not intersect properly, their product vanishes. This gives an analogue of Serre's vanishing result for intersection multiplicities.