The intrinsic stable normal cone
Abstract
We construct an analog of the intrinsic normal cone of Behrend-Fantechi in the equivariant motivic stable homotopy category over a base-scheme B and construct a fundament class in E-cohomology for any cohomology theory E in SH(B). For affine B, a perfect obstruction theory gives rise to a virtual fundamental class in a twisted Borel-Moore E-homology for arbitrary E. This includes motivic cohomology (homotopy invariant) K-theory algebraic cobordism and the oriented Chow groups of Barge-Morel and Fasel. In the case of motivic cohomology, we recover the constructions of Behrend-Fantechi, with values in the Chow group.
Keywords
Cite
@article{arxiv.1703.03056,
title = {The intrinsic stable normal cone},
author = {Marc Levine},
journal= {arXiv preprint arXiv:1703.03056},
year = {2021}
}
Comments
Final version. To appear in "Algebraic Geometry". The paper has been substantially reorganised and hopefully improved. A section on examples has been added. This version corrects some typos