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.

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

References in corpus (2)

• Algebraic cobordism
• The Morel-Voevodsky localization theorem in spectral algebraic geometry

Cited by in corpus (3)

• Fundamental classes in motivic homotopy theory
• Virtual fundamental classes of derived stacks I
• An arithmetic count of the lines meeting four lines in P^3