A New Proof of the New Intersection Theorem
Greg Piepmeyer, Mark E. Walker
TL;DR
This paper presents a new proof of the New Intersection Theorem in mixed characteristic, replacing local Chern characters with Adams operations on K-theory with supports, simplifying the original approach.
Contribution
It provides an alternative proof of the NIT in mixed characteristic, avoiding local Chern characters and employing Adams operations on K-theory instead.
Findings
New proof of NIT in mixed characteristic
Avoids use of local Chern characters
Utilizes Adams operations on K-theory
Abstract
In 1987 Roberts completed the proof of the New Intersection Theorem (NIT) by settling the mixed characteristic case using local Chern characters, as developed by Fulton and also by Roberts. His proof has been the only one recorded of the NIT in mixed characteristic. This paper gives a new proof of this theorem, one which mostly parallels Roberts' original proof, but avoids the use of local Chern characters. Instead, the proof here uses Adams operations on K-theory with supports as developed by Gillet-Soule.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology