On Serre Intersection Multiplicity Conjecture
Mohammad Reza Rahmati
TL;DR
This paper discusses aspects of Serre's intersection multiplicity conjecture and provides a proof for the vanishing of intersection multiplicity in non-proper intersections over regular rings, utilizing Fulton’s intersection theory.
Contribution
It offers a proof of the vanishing of Serre intersection multiplicity in non-proper intersections over regular rings, advancing understanding of the conjecture.
Findings
Proof of vanishing of intersection multiplicity in non-proper cases
Application of Fulton’s intersection theory to Serre's conjecture
Clarification of conditions under which the multiplicity vanishes
Abstract
In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper intersection over a regular ring based on the intersection theory in W. Fulton.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology