English

The intrinsic stable normal cone

Algebraic Geometry 2021-04-13 v3

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

R2 v1 2026-06-22T18:40:17.623Z