A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
K-Theory and Homology
2021-05-20 v2 Algebraic Geometry
Algebraic Topology
Abstract
We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C.
Cite
@article{arxiv.2002.01848,
title = {A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections},
author = {Tom Bachmann and Kirsten Wickelgren},
journal= {arXiv preprint arXiv:2002.01848},
year = {2021}
}
Comments
version accepted for publication in Jussieu